9.3
9.4
9.5
9.6
9.8
100
For the given function find the average rate of change over each specified interval.
f(x) = x2 + x − 12
[−8, 10]
3
100
Find the derivative of the function
y = 8
y' = 0
100
Find the derivative and simplify
y = (6x + 5)(x2 − 3x)
y' = 18x2 - 26x - 15
100
Differentiate the function.
f(x) = (2x3 − 4)18
f'(x) = 108x2(2x3 - 4)17
100
Find the second derivative.
f(x) = 3x10 − 13x5 − 15x3 + 4
f''(x) = 270x8 - 260x3 - 90x
200
If the total revenue function for a blender is R(x) = 34x − 0.01x2 where x is the number of units sold, what is the average rate of change in revenue R(x) as x increases from 10 to 20 units?
337/10
200
Find the derivative of the function
y = 4 − 9x + 3x2
y' = -9 + 6x
200
Find the derivative, but do not simplify your answer
y = (7x6 − 5x4 + 2x2 − 1)(4x9 + 3x7 − 5x2 + 4x)
y' = (7x6 - 5x4 + 2x2 - 1)(36x8 +21x6 - 10x + 4) + (42x5 - 20x3 + 4x)(4x9 + 3x7 -5x2 + 4x)
200
Differentiate the function
200
Find the second derivative
g''(x) = 30x4 - 8x-3
300
Let f(x) = 6x2 − 2x
Find the instantaneous rate of change of f(x) at x = −1
Find the point on the graph of y = f(x) at x = −1
aka (x,y)
Instantaneous Rate of Change = -14
Point on Graph = (-1, 8)
300
Find the derivative of the function
y = x-7 + x-6 − 5
y' = -7x-8 - 6x-7
300
Find the derivative and simplify.
y = (2x7 + 5)(9x6 − 8x4 − 8)
y' = 234x12 - 176x10 - 112x6 + 270x5 -160x3
300
Differentiate the function
300
Find the third derivative.
y = x5 − 13x3 + 17
y''' = 60x2 - 78
400
If the instantaneous rate of change of g(x) at (−1, −1) is 2, write the equation of the line tangent to the graph of g(x) at x = −1
y = 2x + 1
400
Find the derivative of the function
400
Write the equation of the tangent line to the graph of
y = (6x2 − 6x + 2)(1 + 2x) at x = 1
y = 22x - 16
400
Write the equation of the line tangent to the graph of the function at the indicated point.
y = (x2 − 5x + 5)5 at (4, 1)
y = 15x - 59
400
Find the third derivative
y' = 4/x
y''' = 8x-3
500
Use the limit definition of the derivative to find f’ of f(x)=3x2+2
f'(x) = 6x
500
Find the coordinates of points where the graph of
f(x) = −x3 + 9x2 − 15x + 14 has horizontal tangents
There will be two points
(1, 7)
(5, 39)
500
Write the equation of the tangent line to the graph of
y = (7x2 − 6x + 1)(1 + 2x) at x = 1
y = 28x - 22
500
The revenue from the sale of a product is, in dollars,
R = 1500x + 3000(5x + 3)-1 − 1000
where x is the number of units sold. Find the marginal revenue when 250 units are sold. (Round your answer to two decimal places.)
1499.99
500
The revenue (in dollars) from the sale of x units of a certain product can be described by
R(x) = 100x − 0.01x2
Find the instantaneous rate of change of the marginal revenue
R''(x) = -0.02