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

Find the derivative....SIMPLIFY FIRST!

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

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Calculus: Power Rule and Product Rule

22 termsStudBud Administration58 plays

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

Flashcards22 cardsFPractice quizPHost liveL

Questions 22

Answers

1
Find an equation of the Tangent Line at the given point f(x) = (x +3)(x² - 2) at (-2, 2)
y - 2 = -2(x + 2)
y - 2 = -2(x - 2)
y + 2 = -2(x + 2)
y + 2 = 2(x - 2)
2
Find the average rate of change of f(x) = x ²+ 2x over the interval (1, 2)
6
4
7
5
3
Find the derivative.
f'(x) = (1/2)x - (-1/2)x
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
f'(x) = 1/(2x1/2) - 1/(2x3/2)
f'(x) = 1/(2x1/2) + 1/(2x3/2)
4
Find the derivative.
f'(t) = -3t2cos(t) + t3sin(t)
f'(t) = 3t2cos(t) + t3sin(t)
f'(t) = 3t2cos(t) - t3sin(t)
f'(t) = -3t2sin(t)
5
Find the derivative of \left(3x-2x^2\right)\left(5+4x\right)
-24x^{2^{ }}-4x+15
-24x^2-4x-15
-24x^2+4x+15
24x^{^2}+4x+15
6
Find f'(1) if f(x) = (x² - 2x +1)(x³ - 1)
3
0
2
1
7
Determine the x-value(s), if any, at which f (x) = x ³ + 6x - 2 has a horizontal tangent.
x = -2
The graph has no horizontal tangents
x = 2
x = 3
8
At which x - value(s) is the graph shown not differentiable?
x = 0
x =1
x = 0 and x =1
x = -2 and x = 2
9
This is an actual pitcher for the Chicago Cubs
False
True
10
Name this future Hall of Famer...
Justice Fields
Justin Fields
Justice Field
Justin Field
11
Find f'(x) if f(x) = 3x²(sinx)
3x2cosx + 6xsinx
-3x2cosx - 6xsinx
-3x2sinx - 6xcosx
3x2sinx + 6xcosx
12
Find the derivative.
f'(t) = 3cos(t) - (1/4)sin(t)
f'(t) = -3sin(t) - (1/4)cos(t)
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = 3sin(t) + (1/4)cos(t)
13
Let f (x) = x⁴+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
3
7
10
4
14
Find the derivative....SIMPLIFY FIRST!
f'(x) = -1/(2x3/2) - 12x2 - 3/x2
f'(x) = x-1/2 - 12x2 + 3x-1
f'(x) = 1/(2x1/2) - 12x2 - 3/x2
f'(x) = -1/(2x3/2) - 12x2 + 3/x2
15
Find the derivative....SIMPLIFY FIRST!
y' = (6x2 - 6x + 4)/(2x)
f'(x) = 3x - 3 + 2/x
f'(x) = 2x - 3 + 4/x
f'(x) = 2 - 4/x2
16
Who's this?!
Singer of "Fins"
Singer of I'm Yours"
Singer of "I Saw the Sine"
Singer of "I've Got The Power!"
17
Find the derivative of f(x) = x⁴ + 5x
f ' (x) = 12x3 + 5x
f ' (x) = 4x3
f ' (x) = 4x3 + 5
f ' (x) = 4x2 + 5
18
Find y' if y = 2x(cosx)
-2xcosx + 2sinx
-2xsinx + 2cosx
2xcosx - 2sinx
2xsinx + 2cosx
19
Who's the guy on the right?
Your current HPC teacher
Who cares?!
Model for JC Penney
Who knows?!
20
Find the derivative of y = π
DNE
pi
1
0
21
Find the derivative of f(x) = 7x^-1
f ' (x) = -7x-2
f ' (x) = -7x
f ' (x) = 7x-2
f ' (x) = -7x-1
22
Find the derivative...SIMPLIFY FIRST!
f'(t) = (-4/3)t3
f'(t) = 4/(3t3)
f'(t) = -4/(3t3)
f'(t) = (4/3)t

Calculus: Power Rule and Product Rule Flashcards | StudBud

Calculus: Power Rule and Product Rule

22 termsStudBud Administration58 plays

Flashcards22 cardsFPractice quizPHost liveL

Questions 22

Answers

1
Find an equation of the Tangent Line at the given point f(x) = (x +3)(x² - 2) at (-2, 2)
y - 2 = -2(x + 2)
y - 2 = -2(x - 2)
y + 2 = -2(x + 2)
y + 2 = 2(x - 2)
2
Find the average rate of change of f(x) = x ²+ 2x over the interval (1, 2)
6
4
7
5
3
Find the derivative.
f'(x) = (1/2)x - (-1/2)x
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
f'(x) = 1/(2x1/2) - 1/(2x3/2)
f'(x) = 1/(2x1/2) + 1/(2x3/2)
4
Find the derivative.
f'(t) = -3t2cos(t) + t3sin(t)
f'(t) = 3t2cos(t) + t3sin(t)
f'(t) = 3t2cos(t) - t3sin(t)
f'(t) = -3t2sin(t)
5
Find the derivative of \left(3x-2x^2\right)\left(5+4x\right)
-24x^{2^{ }}-4x+15
-24x^2-4x-15
-24x^2+4x+15
24x^{^2}+4x+15
6
Find f'(1) if f(x) = (x² - 2x +1)(x³ - 1)
3
0
2
1
7
Determine the x-value(s), if any, at which f (x) = x ³ + 6x - 2 has a horizontal tangent.
x = -2
The graph has no horizontal tangents
x = 2
x = 3
8
At which x - value(s) is the graph shown not differentiable?
x = 0
x =1
x = 0 and x =1
x = -2 and x = 2
9
This is an actual pitcher for the Chicago Cubs
False
True
10
Name this future Hall of Famer...
Justice Fields
Justin Fields
Justice Field
Justin Field
11
Find f'(x) if f(x) = 3x²(sinx)
3x2cosx + 6xsinx
-3x2cosx - 6xsinx
-3x2sinx - 6xcosx
3x2sinx + 6xcosx
12
Find the derivative.
f'(t) = 3cos(t) - (1/4)sin(t)
f'(t) = -3sin(t) - (1/4)cos(t)
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = 3sin(t) + (1/4)cos(t)
13
Let f (x) = x⁴+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
3
7
10
4
14
Find the derivative....SIMPLIFY FIRST!
f'(x) = -1/(2x3/2) - 12x2 - 3/x2
f'(x) = x-1/2 - 12x2 + 3x-1
f'(x) = 1/(2x1/2) - 12x2 - 3/x2
f'(x) = -1/(2x3/2) - 12x2 + 3/x2
15
Find the derivative....SIMPLIFY FIRST!
y' = (6x2 - 6x + 4)/(2x)
f'(x) = 3x - 3 + 2/x
f'(x) = 2x - 3 + 4/x
f'(x) = 2 - 4/x2
16
Who's this?!
Singer of "Fins"
Singer of I'm Yours"
Singer of "I Saw the Sine"
Singer of "I've Got The Power!"
17
Find the derivative of f(x) = x⁴ + 5x
f ' (x) = 12x3 + 5x
f ' (x) = 4x3
f ' (x) = 4x3 + 5
f ' (x) = 4x2 + 5
18
Find y' if y = 2x(cosx)
-2xcosx + 2sinx
-2xsinx + 2cosx
2xcosx - 2sinx
2xsinx + 2cosx
19
Who's the guy on the right?
Your current HPC teacher
Who cares?!
Model for JC Penney
Who knows?!
20
Find the derivative of y = π
DNE
pi
1
0
21
Find the derivative of f(x) = 7x^-1
f ' (x) = -7x-2
f ' (x) = -7x
f ' (x) = 7x-2
f ' (x) = -7x-1
22
Find the derivative...SIMPLIFY FIRST!
f'(t) = (-4/3)t3
f'(t) = 4/(3t3)
f'(t) = -4/(3t3)
f'(t) = (4/3)t