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Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.

Study the graph. You can see the curve at 0 and increasing indefinitely and vice versa.  

Same here. Study the graph.
You can see the curve at positive 2 and increasing indefinitely and vice versa.
 
Same here. Study the graph Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
 

Same here. Study the graph  
Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
 

Same here. Study the graph Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
 

Same here. Study the graph  
Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
 
Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
 
Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
 
Find the open intervals where the function graphed below is​ (a)​ increasing, or​ (b) decreasing.
 

 
Study the graph and answers!
   
Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.

 
Study the graph and answers!
  Find the open intervals where the function graphed below is ​a)​ increasing, or ​b) decreasing.
 

 
Study the graph and answers!
   
Find the locations and values of all relative extrema for the function with the graph below.
 

Study the graph and answers!
   
Find the locations and values of all relative extrema for the function with the graph below.
 

 
Study the graph and answers!
   
For the function​ below, find (​a) the critical​ numbers; (​b) the open intervals where the function is​ increasing;
and (​c) the open intervals where it is decreasing.   f(x) = 2.7 + 3.4x – 0.7x²
 

 
2.7 + 3.4x – 0.7x²
-1.4x + 3.4
-1.4x + 3.4 = 0
-1.4x = -3.4
x = 3.4/1.4
 
Check
https://www.emathhelp.net/calculators/calculus-1/function-calculator
2.7 + 3.4x – 0.7x²
   
For the function​ below, find (​a) the critical​ numbers; (​b) the open intervals where the function is​ increasing; and
(​c) the open intervals where it is decreasing.   x^{3 -} 6x² – 216x – 28
 

 
a. explanation
Find the derivative of x³ - 6x2 – 216x – 28
You should know how to find the derivative of a function by now.
So, the derivative of x³ - 6x2 – 216x – 28 =             4x² – 12x – 216
Now we set the derivative to equal zero
4x² – 12x – 216 = 0
 
https://quickmath.com/
4x² – 12x – 216 = 0
x = -6, 9   So, the critical numbers are -6, 9
 
Check
https://www.emathhelp.net/en/calculators/calculus-1/critical-points-extrema-calculator/
x³ - 6x² – 216x – 28
   
For the function​ below, find a) the critical​ numbers; b) the open intervals where the function is​ increasing; and ​
c) the open intervals where it is decreasing.            f(x) = 8x³ – 42x² – 360x + 4
 

 
Find the derivative of 8x³ – 42x² – 360x + 4 =           24x² – 84x
Set = 0
24x² – 84x -360 = 0
https://quickmath.com/
The critical Numbers are 6, -5/2
 
Check
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
8x³ – 42x² – 360x+4
   
For the function​ below, find (​a) the critical​ numbers; (​b) the open intervals where the function is​ increasing;
and  (​c) the open intervals where it is decreasing.              f(x) = 2.5 + 2.2x – 0.6x²
 

 
 
Find the derivative of 2.5 + 2.2x – 0.6x^{2 =}
https://www.emathhelp.net/calculators/calculus-1/function-calculator
   
For the function​ below, find (​a) the critical​ numbers; (​b) the open intervals where the function is​ increasing; and (​c) the open intervals where it is decreasing
 

https://www.emathhelp.net/calculators/calculus-1/function-calculator
a.      Critical points are the values of x and x.
b.      Intervals of Increase as stated in results
c.       Decreasing - Intervals of Decrease as stated
   
For the function​ below, find
​(​a) the critical​ numbers;
​(​b) the open intervals where the function is​ increasing; and
​(​c) the open intervals where it is decreasing.
https://www.emathhelp.net/calculators/calculus-1/function-calculator
 
a = 2^nd and first numbers of Intervals of Increase
b = Intervals of Increase (common (),() )
c = Intervals of Decrease
 
 
For the following​ function, find​ a) the critical​ numbers, b) the open intervals where the function is​ increasing,
and​ c) the open intervals where it is decreasing.
y = -3x - 10
 

 
Check
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
   
For the function​ below, find ​a) the critical​ numbers; ​b) the open intervals where the function is​ increasing;
and ​c) the open intervals where it is decreasing.

 
 
 
   
For the function​ below, find a) the critical​ numbers b) the open intervals where the function is​
increasing c) the open intervals where it is decreasing.
f(x) = (x + 7)^2/3
 
 
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
a = Intervals of Increase = first number
b = Intervals of Increase
c = Intervals of decrease
  Where is the function defined by f(x) = ln (x) increasing? Where is f(x) = ln (x) decreasing? Where is the tangent line​ horizontal?
Find derivative and value of x = 0
 
Suppose the total cost​ C(x) (in​ dollars) to manufacture a quantity x of weed killer​ (in hundreds of​ liters) is given by the function.
C(x) = x³ – 4x² + 9x + 50
 

 
You can graph this or check
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
x^3– 4x^2+9x+50
Scroll down to
Critical Points
Local Minima
Local Maxima  
A manufacturer sells video games with the following cost and revenue functions​ (in dollars),
where x is the number of games sold. Determine the​ interval(s) on which the profit function is increasing.

 

R(x) – C(x)
.326x² - .11x² = .216x²
.0002x³ - .00016 = .00004x³
.216x² - .00004x³
find the derivative of
.216x² - .00004x³ = .432x - .00012x²
 
.432x - .00012x² = 0
 x = 0 or x = 3600
answer = (0,3600)
   
Find the locations and values of all relative extrema for the function with the graph below.


Study the graph
  Find the locations and values of all relative extrema for the function with the graph below.
 


Study the graph
   
Find the locations and values of all relative extrema for the function with the graph below.
 

Study the graph
  Find the locations and values of all relative extrema for the function with the graph below.

Study the graph
  Find the locations and values of all relative extrema for the function with the graph below.

Study the graph
  Suppose that the graph below is the graph of f(x) right parenthesis, the derivative of f(x) right parenthesis.
Find the locations of all relative​ extrema and tell whether each extremum is a relative maximum or minimum.

Study the graph
  Suppose that the graph below is the graph of f’(x), the derivative of f(x).
Find the locations of all the relative extrema and tell whether each extremum is a relative maximum or minimum.
 

Study the graph Find the​ x-values of all points where the function has any relative extrema. Find the​ value(s) of any relative extrema.
f(x) = -x³ – 3x² + 9x - 1

Long way:
Find derivative of f(x) = -x³ – 3x² + 9x – 1 =               -3x² – 6x + 9
Set equation = zero
-3x² – 6x + 9 = 0
https://quickmath.com/                   enter -3x^2–6x+9=0
x = 1, -3
Plug in the values of x
Maximum
-(1)³ – 3(1)² + 9(1) – 1 = 4
Minimum
-(-3)³ – 3(-3)² + 9(-3) – 1 = -28
 
Check
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
-x^3 – 3x^2 + 9x - 1
enter equation then,
Local Maxima
Local Minima
  Find the​ x-values of all points where the function has any relative extrema. Find the​ value(s) of any relative extrema.
f(x) = x³ – 3x² – 24x - 4

 
This is the same.
Find the derivative of x³ – 3x² – 24x – 4 =     3x² – 6x – 24
Set = 0
3x² – 6x – 24 = 0
https://quickmath.com
3x^2-6x-25=0
x = -2, 4
(-2)³ – 3(-2)² – 24(-2) - 4
Check
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
You want to enter
x^3-3x^2-24x-4
Local Maxima
Local Minima
  Find the​ x-values of all points where the function has any relative extrema. Find the​ value(s) of any relative extrema.
f(x) = x⁴ – 32x² - 2
 

 
First find the derivative of​ f(x)
4x³ – 64x
 
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
enter equation then,
Critical Points (x = first numbers)
 
Local Maxima
First number is x second number is maximum.
 
Local Minima
First numbers are x values, second are minimums
  Find the​ x-values of all points where the function has any relative extrema. Find the​ value(s) of any relative extrema.
F(x) = 8 – (3 + 3x)^2/3
 
 

https://www.emathhelp.net/calculators/calculus-1/function-calculator/
enter equation then,
Local Maxima
First number is x second number is maximum.
Local Minima
First numbers are x values, second are minimums.
  Find the​ x-values of all points where the function has any relative extrema. Find the​ value(s) of any relative extrema

 

https://www.emathhelp.net/calculators/calculus-1/function-calculator/
(x^2–16x+64)/(x–10)
Local Maxima
First number is x second number is maximum.
Local Minima
First numbers are x values, second are minimums.
  Find the​ x-values of all points where the function has any relative extrema. Find the​ value(s) of any relative extrema.
f(x) = -7x – 4 ln(x)

 
Find the derivative
-7x – 4 ln(x)
The derivative of ln(x) with respect to x is
So, the derivative =  – 7
 
Check
https://www.emathhelp.net/calculators/calculus-1/function-calculator/
enter equation in ()
 
Critical Points
Local Maxima
First number is x second number is maximum.
Local Minima
First numbers are x values, second are minimums.

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