AP Calculus Unit 2 Review

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

• 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 has a sharp turn in the first quadrant so if is not differentiable.

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

Tags

CCSS.HSA.REI.D.10

In which quadrant of the graph above will there be a value of x that is non-differentiable?

• 1

• 2

• 3

• 4

Tags

CCSS.8.F.A.3

Is the above function differentiable at x = 0? Why?

• No. The $\lim_{h\rightarrow0}\frac{\left(\left(x+h\right)^{\frac{2}{3}}-\left(x\right)^{\frac{2}{3}}\right)}{h}$ does not exist.

• Yes. The $\lim_{h\rightarrow0}\frac{\left(\left(x+h\right)^{\frac{2}{3}}-\left(x\right)^{\frac{2}{3}}\right)}{h}$ exists.

• Yes. The $\lim_{x\rightarrow0}\ x^{\frac{2}{3}}=0$ from the left and the right.

• No. The $\lim_{x\rightarrow0}\ x^{\frac{2}{3}}=0$ doesn't exist since the left and right hand limits are not the same.

Is the above function differentiable at

x = 0? Why?

• Yes. The derivative would be equal to zero since there is a vertical tangent.

• No. The derivative would not exist at x = 0 since there is a vertical tangent.

• No. The derivative does not exist since $\lim_{x\rightarrow0}\ x^{\frac{1}{3}}$ does not exist.

• Yes since $\lim_{h\rightarrow0}\ \frac{\left(x+h\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{h}$ exists.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

• The graph contains a corner.

• The graph contains a cusp.

• The graph contains a discontinuity.

• The graph contains a vertical tangent.

Tags

CCSS.8.F.A.3

If  $f\left(x\right)$  has a derivative at x = a, then f is continuous at x = a.

• True

• False

For what value(s) of x is the function continuous but not differentiable?

• x = -1

• x = 0

• x = 2

• x = 3; x = -2

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

For what values of x in the domain of the above function does the function to appear differentiable?

• (-2, 3)

• All real numbers.

• [-2, 3]

• $x\ge0$

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.5

CCSS.HSF.IF.A.1

The graph of a function is given. Which of the following is not true

• Function is continuous at x = 2

• Function is differentiable at x = 2

• Function has a limit that exists at x = 2

• Function exists at x = 2

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.5

CCSS.HSF.IF.A.1

Does the mean value theorem apply to f on [0, 5] ?

• yes

• no

Tags

CCSS.HSF.IF.B.6