Determine the x-value(s), if any, at which f (x) = x 3 + 6x - 2 has a horizontal tangent.

The graph has no horizontal tangents

f'(x) = -1/(2x3/2) - 12x2 - 3/x2

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Calculus Basic Derivative Rules

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AP Calculus Basic Derivatives: Power Rule and Graphs of Derivatives Basic Derivative Rules: Quiz over the basic derivative rules including powe as well as sin, cos, tan

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Questions 18

Answers

1
Find the derivative
pi
1
DNE
0
2
Find the derivative.
f'(x) = 1/(2x1/2) + 1/(2x3/2)
f'(x) = (1/2)x - (-1/2)x
f'(x) = 1/(2x1/2) - 1/(2x3/2)
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
3
Find the derivative.
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = 3cos(t) - (1/4)sin(t)
f'(t) = 3sin(t) + (1/4)cos(t)
f'(t) = -3sin(t) - (1/4)cos(t)
4
Find the derivative of f(x) = x⁴ + 5x
f ' (x) = 4x3
f ' (x) = 4x3 + 5
f ' (x) = 4x2 + 5
f ' (x) = 12x3 + 5x
5
Find the derivative of f(x) = 4x^1/2+ 2
f ' (x) = 8x-1/2 + 2
f ' (x) = 8x-1/2
f ' (x) = 2x1/2
f ' (x) = 2x-1/2
6
Let f (x) = 6x^1/2. What is the instantaneous rate of change at x = 4?
6
3/4
3
3/2
7
Horizontal tangents?
x = -6, x = 2
x = 3
x = 3, x = 4
x = 6, x = -2
8
Determine the x-value(s), if any, at which f (x) = x ³ + 6x - 2 has a horizontal tangent.
x = 3
x = -2
x = 2
The graph has no horizontal tangents
9
Find the derivative.
f'(x) = 2 - 4/x2
f'(x) = 3x - 3 + 2/x
f'(x) = 2x - 3 + 4/x
y' = (6x2 - 6x + 4)/(2x)
10
Let f (x) = -2x³ + x² - 4x. What is the slope of the tangent line at x = 2 ?
-24
-16
24
16
11
At which x - value(s) is the graph shown not differentiable?
x = 0 and x =1
x =1
x = 0
x = -2 and x = 2
12
Find the derivative.
f'(t) = (-4/3)t3
f'(t) = (4/3)t
f'(t) = 4/(3t3)
f'(t) = -4/(3t3)
13
Let f (x) = x⁴+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
7
4
3
10
14
Find the derivative.
f'(x) = -1/(2x3/2) - 12x2 + 3/x2
f'(x) = 1/(2x1/2) - 12x2 - 3/x2
f'(x) = -1/(2x3/2) - 12x2 - 3/x2
f'(x) = x-1/2 - 12x2 + 3x-1
15
Find the derivative of f(x) = 7x^-1
f ' (x) = -7x
f ' (x) = -7x-1
f ' (x) = -7x-2
f ' (x) = 7x-2
16
Find the average rate of change of f(x) = x ²+ 2x over the interval (1, 2)
7
6
4
5
17
Given f (x) = x⁴+ x³- x + 1, what is f ' (1) ?
2
6
8
7
18
Find the derivative.
f'(x) = 3x2 - 6x
f'(x) = -3x
f'(x) = 3x2 - 6
f'(x) = 0

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