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) = (-x2 + 6x + 1)/(x2 + 1)2

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

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Product, Quotient, Chain Derivatives

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

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Questions 24

Answers

1
Horizontal tangents?
x = 3
x = 6, x = -2
x = 3, x = 4
x = -6, x = 2
2
Find the derivative
pi
DNE
0
1
3
Find the derivative.
f'(x) = 2 - 4/x2
f'(x) = 2x - 3 + 4/x
y' = (6x2 - 6x + 4)/(2x)
f'(x) = 3x - 3 + 2/x
4
Determine the x-value(s), if any, at which f (x) = x ³ + 6x - 2 has a horizontal tangent.
x = 3
x = -2
The graph has no horizontal tangents
x = 2
5
Let f (x) = x⁴+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
4
3
10
7
6
Find the derivative.
f'(x) = 1/(2x1/2) + 1/(2x3/2)
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
f'(x) = 1/(2x1/2) - 1/(2x3/2)
f'(x) = (1/2)x - (-1/2)x
7
Let f (x) = 6x^1/2. What is the instantaneous rate of change at x = 4?
3
3/2
3/4
6
8
Find the derivative.
f'(t) = (-4/3)t3
f'(t) = (4/3)t
f'(t) = -4/(3t3)
f'(t) = 4/(3t3)
9
Find the derivative.
f'(t) = -3t2sin(t)
f'(t) = 3t2cos(t) - t3sin(t)
f'(t) = 3t2cos(t) + t3sin(t)
f'(t) = -3t2cos(t) + t3sin(t)
10
Find the derivative of f(x) = 7x^-1
f ' (x) = -7x-2
f ' (x) = -7x
f ' (x) = -7x-1
f ' (x) = 7x-2
11
Find the derivative.
f'(x) = (-x2 - 6x + 1)/(x2 + 1)2
f'(x) = -x2 + 6x + 1
f'(x) = 1/(2x)
f'(x) = (-x2 + 6x + 1)/(x2 + 1)2
12
Let f (x) = -2x³ + x² - 4x. What is the slope of the tangent line at x = 2 ?
-24
16
-16
24
13
Given f (x) = x⁴+ x³- x + 1, what is f ' (1) ?
2
6
7
8
14
Find the derivative.
f'(x) = 1/(2x1/2) - 12x2 - 3/x2
f'(x) = x-1/2 - 12x2 + 3x-1
f'(x) = -1/(2x3/2) - 12x2 - 3/x2
f'(x) = -1/(2x3/2) - 12x2 + 3/x2
15
Find the derivative.
y' = 2 - 2xtan(x) - x2sec(x)tan(x)
y' = 2 - 2x sec2(x)
y' = 2 - 2xtan(x) - x2sec2(x)
y' = 2 - 2x sec(x)tan(x)
16
Find the derivative.
y' = 12x2(x2 - 1)2
y' = (2x)(x2 - 1)2(4x2 - 1)]
Nope
y' = (x2 - 1)2[2x(x2 - 1) + 3x2]
17
Find the average rate of change of f(x) = x ²+ 2x over the interval (1, 2)
5
7
4
6
18
Find the average rate of change.
1
1/2
-3/2
3/2
19
At which x - value(s) is the graph shown not differentiable?
x =1
x = -2 and x = 2
x = 0
x = 0 and x =1
20
Find the derivative of f(x) = x⁴ + 5x
f ' (x) = 12x3 + 5x
f ' (x) = 4x3
f ' (x) = 4x2 + 5
f ' (x) = 4x3 + 5
21
Find the derivative.
f'(x) = -3x2/[2(1 - x3)1/2]
f'(x) = (1-x3)1/2
f'(x) = (1/2)/(1 - x3)1/2
f'(x) = sqr(-3x2)
22
Find the derivative of f(x) = 4x^1/2+ 2
f ' (x) = 2x1/2
f ' (x) = 2x-1/2
f ' (x) = 8x-1/2 + 2
f ' (x) = 8x-1/2
23
Find the derivative.
f'(x) = 3x2 - 6x
f'(x) = 3x2 - 6
f'(x) = -3x
f'(x) = 0
24
Find the derivative.
f'(t) = -3sin(t) - (1/4)cos(t)
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = 3sin(t) + (1/4)cos(t)
f'(t) = 3cos(t) - (1/4)sin(t)

Product, Quotient, Chain Derivatives Flashcards | StudBud

Product, Quotient, Chain Derivatives

24 termsStudBud Administration9 plays

Flashcards24 cardsFPractice quizPHost liveL

Questions 24

Answers

1
Horizontal tangents?
x = 3
x = 6, x = -2
x = 3, x = 4
x = -6, x = 2
2
Find the derivative
pi
DNE
0
1
3
Find the derivative.
f'(x) = 2 - 4/x2
f'(x) = 2x - 3 + 4/x
y' = (6x2 - 6x + 4)/(2x)
f'(x) = 3x - 3 + 2/x
4
Determine the x-value(s), if any, at which f (x) = x ³ + 6x - 2 has a horizontal tangent.
x = 3
x = -2
The graph has no horizontal tangents
x = 2
5
Let f (x) = x⁴+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
4
3
10
7
6
Find the derivative.
f'(x) = 1/(2x1/2) + 1/(2x3/2)
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
f'(x) = 1/(2x1/2) - 1/(2x3/2)
f'(x) = (1/2)x - (-1/2)x
7
Let f (x) = 6x^1/2. What is the instantaneous rate of change at x = 4?
3
3/2
3/4
6
8
Find the derivative.
f'(t) = (-4/3)t3
f'(t) = (4/3)t
f'(t) = -4/(3t3)
f'(t) = 4/(3t3)
9
Find the derivative.
f'(t) = -3t2sin(t)
f'(t) = 3t2cos(t) - t3sin(t)
f'(t) = 3t2cos(t) + t3sin(t)
f'(t) = -3t2cos(t) + t3sin(t)
10
Find the derivative of f(x) = 7x^-1
f ' (x) = -7x-2
f ' (x) = -7x
f ' (x) = -7x-1
f ' (x) = 7x-2
11
Find the derivative.
f'(x) = (-x2 - 6x + 1)/(x2 + 1)2
f'(x) = -x2 + 6x + 1
f'(x) = 1/(2x)
f'(x) = (-x2 + 6x + 1)/(x2 + 1)2
12
Let f (x) = -2x³ + x² - 4x. What is the slope of the tangent line at x = 2 ?
-24
16
-16
24
13
Given f (x) = x⁴+ x³- x + 1, what is f ' (1) ?
2
6
7
8
14
Find the derivative.
f'(x) = 1/(2x1/2) - 12x2 - 3/x2
f'(x) = x-1/2 - 12x2 + 3x-1
f'(x) = -1/(2x3/2) - 12x2 - 3/x2
f'(x) = -1/(2x3/2) - 12x2 + 3/x2
15
Find the derivative.
y' = 2 - 2xtan(x) - x2sec(x)tan(x)
y' = 2 - 2x sec2(x)
y' = 2 - 2xtan(x) - x2sec2(x)
y' = 2 - 2x sec(x)tan(x)
16
Find the derivative.
y' = 12x2(x2 - 1)2
y' = (2x)(x2 - 1)2(4x2 - 1)]
Nope
y' = (x2 - 1)2[2x(x2 - 1) + 3x2]
17
Find the average rate of change of f(x) = x ²+ 2x over the interval (1, 2)
5
7
4
6
18
Find the average rate of change.
1
1/2
-3/2
3/2
19
At which x - value(s) is the graph shown not differentiable?
x =1
x = -2 and x = 2
x = 0
x = 0 and x =1
20
Find the derivative of f(x) = x⁴ + 5x
f ' (x) = 12x3 + 5x
f ' (x) = 4x3
f ' (x) = 4x2 + 5
f ' (x) = 4x3 + 5
21
Find the derivative.
f'(x) = -3x2/[2(1 - x3)1/2]
f'(x) = (1-x3)1/2
f'(x) = (1/2)/(1 - x3)1/2
f'(x) = sqr(-3x2)
22
Find the derivative of f(x) = 4x^1/2+ 2
f ' (x) = 2x1/2
f ' (x) = 2x-1/2
f ' (x) = 8x-1/2 + 2
f ' (x) = 8x-1/2
23
Find the derivative.
f'(x) = 3x2 - 6x
f'(x) = 3x2 - 6
f'(x) = -3x
f'(x) = 0
24
Find the derivative.
f'(t) = -3sin(t) - (1/4)cos(t)
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = 3sin(t) + (1/4)cos(t)
f'(t) = 3cos(t) - (1/4)sin(t)