d d x ( a x ) = \frac{\text{d}}{\text{d}x}\left(a^x\right)= d x d ( a x ) =

1 x ln ⁡ a \frac{1}{x\ln a} x ln a 1

Set up the derivative of y=(3x 4 - 7)*(5x 2 + 1)

(3x 4 - 7)*(10x) + (12x 3 )*(5x 2 + 1)

(3x 4 - 7)*(10x) - (12x 3 )*(5x 2 + 1)

(3x 4 - 7)/(10x) + (12x 3 )/(5x 2 + 1)

Is the above function differentiable for all values of x? Why?

No, the function has a sharp turn in the first quadrant so if is not differentiable.

Yes, the slope of the tangent line can be calculated for all values of x.

Yes, the function is continuous for all values of x so the function is differentiable.

No, the function is discontinuous so it is not differentiable.

At x = 1, the function shown is ...

Neither continuous nor differentiable.

Continuous but not differentiable.

Differentiable but not continuous.

Both continuous and differentiable.

The derivative of a function is its

Instantaneous rate of change at any point in its domain

$$\lim_{x\rightarrow1}\ \frac{\sqrt{x^2+3x}-2}{x-1}$$ is the instantaneous rate of change of what function at what value of the domain?

$$f\left(x\right)=\sqrt{x^2-3x}$$ at $$x=1$$

$$f\left(x\right)=\sqrt{x^2-3x}-2$$ at $$x=1$$

$$f\left(x\right)=\sqrt{x^2-3x}$$ at $$x=2$$

$$f\left(x\right)=\frac{\sqrt{x^2-3x}}{x-1}$$ at $$x=1$$

If a function is differentiable, it is also continuous.

It all depends on the function in question.

has a limit that exists at x = 8

has a limit that exists at x = 2

Which of the following would be a valid reason the above function is non-differentiable at x = 0?

The graph contains a discontinuity.

The graph contains a vertical tangent.

AP Calculus AB Unit 2 Review: 70-Question Practice Test

70 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Find the second derivative of the function:
f (x) = 2x - 5x⁶

f ''(x)= 2 - 30x

f ''(x) = 2-30x⁵

f ''(x) = -30x⁵

f ''(x) = -150x⁴

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Average Rate of Change

Average Value of f

Intermediate Value Theorem

Rolle's Theorem

Which if the following is not a correct notation for 'derivative?'

f'(x)

y'

dy

dy/dx

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find f'(x) if f(x)=x²

2x

x²

2

2x²

How do you find horizontal tangent lines?

Find where the derivative is undefined

Find where the derivative equals zero

Find where the derivative is 1

Find where the derivative is negative

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Derivative means the same thing as

slope of the tangent line

slope of the normal line

exponent

potato

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If a function has a derivative that is negative, what does that tell you?

The function is increasing

The function is decreasing

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

True or False: If $f$ has a derivative at $x\ =\ a$ , then $f$ is continuous at $x\ =\ a$ ?

False

True

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AP Calculus AB Unit 2 Review

Find the second derivative of the function:f (x) = 2x - 5x6

Which if the following is not a correct notation for 'derivative?'

Find f'(x) if f(x)=x2

How do you find horizontal tangent lines?

Derivative means the same thing as

If a function has a derivative that is negative, what does that tell you?

Given the function graphed, which is the graph of the derivative?

True or False: If fff has a derivative at x = ax\ =\ ax = a , then fff is continuous at x = ax\ =\ ax = a ?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find the second derivative of the function:
f (x) = 2x - 5x⁶

Find f'(x) if f(x)=x²

True or False: If $f$ has a derivative at $x\ =\ a$ , then $f$ is continuous at $x\ =\ a$ ?