Question 1

If $f$ has a derivative at $x=a$ , then $f$ is continuous at $x=a$ .

Accepted Answer

True

Answer

False

Answer

It depends on the given condition

Answer

Sometimes

Question 2

A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a...

Accepted Answer

corner, cusp (point or edge), vertical tangent, discontinuity

Answer

corner, curve, vertical tangent, discontinuity

Answer

corner, curve, horizontal tangent, continuity

Answer

corner, cusp (point or edge), horizontal tangent, continuity

Question 3

Where is the graph continuous yet NOT differentiable?

Accepted Answer

x = b, d

Answer

x = a, b

Answer

x = b, c, d

Answer

x = a, b, c, d

Question 4

At $f$ , the function given by $x=a$ is...

Accepted Answer

Continuous but Not Differentiable

Answer

Not Continuous but Differentiable

Answer

Not Continuous and Not Differentiable

Answer

Continuous and Differentiable

Question 5

Differentiability implies continuity.

Accepted Answer

True

Answer

Cannot be determined

Answer

False

Answer

Sometimes

Question 6

Find the derivative of $f$

Accepted Answer

-4

Answer

4

Answer

0

Answer

x

Question 7

What is the derivative of $f$ ?

Accepted Answer

Answer

Answer

Answer

Question 8

What is the derivative of $f$ ?

Accepted Answer

Answer

<math>\left(n-1\right)x^n</math>

Answer

<math>\left(n+1\right)x^{n-1}</math>

Answer

Question 9

What is the derivative of $f$

Accepted Answer

0

Answer

7x

Answer

7

Answer

14

Question 10

What is the derivative of $f$ ?

Accepted Answer

Answer

<math>\ln\left(x+1\right)</math>

Answer

Answer

Question 11

The function in the graph shown below...

Accepted Answer

is continuous and differentiable at x = 2

Answer

is not continuous but differentiable at x = 2

Answer

has a limit that does not exist at x = 2

Answer

is continuous but not differentiable at x = 2

Question 12

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

Accepted Answer

The graph contains a discontinuity.

Answer

The graph contains a corner.

Answer

The graph contains a vertical tangent.

Answer

The graph contains a cusp (edge or point).

Question 13

What prevents an equation from being differentiable?

Accepted Answer

All of these

Answer

Jump discontinuity

Answer

Cusp

Answer

Vertical tangent line

Question 14

At $f$ , the function given by $x=a$

Accepted Answer

Continuous but Not Differentiable

Answer

Not Continuous but Differentiable

Answer

Continuous and Differentiable

Answer

Not Continuous and Not Differentiable

Question 15

The function shown in the graph...

Accepted Answer

has a limit that exists at x = 4

Answer

is differentiable at x = 4

Answer

is continuous at x = 4

Answer

is continuous and differentiable at x = 4

Question 16

Find the derivative of $f$

Accepted Answer

Answer

Answer

Answer

Question 17

Find the derivative: $f$

Accepted Answer

Answer

Answer

Answer

Question 18

What rule should be used in deriving $f$ ?

Accepted Answer

Power rule

Answer

Constant rule

Answer

Difference rule

Answer

Sum rule

Question 19

Find <math>\frac{dx}{dy}\ e^{3x}</math>.

Accepted Answer

Answer

Answer

Answer

Question 20

What is the derivative of $f$

Accepted Answer

Answer

Answer

Answer

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