Differentiability Multiple Choice Practice

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

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

Find all points of the domain of  $y\ =\ \left|x-2\right|+3$  where  $\frac{dy}{dx}$  does not exist. 

•  $\frac{dy}{dx}$  exists for all real numbers.

•  $\frac{dy}{dx}$  does not exist at (0,0).

•  $\frac{dy}{dx}$  does not exist at (2,3).

•   $\frac{dy}{dx}$  does not exist at (-2,3).

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

Graph of a function is given.Where is the function continuous yet NOT differentiable?

• x = a, b, c, d

• x = b, c, d

• x = a, b,

• x = b, d

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The function shown

• is continuous at x = 4

• is differentiable at x = 4

• has a limit that exists at x = 4

• exists at x = 4

(Select all that apply) The function shown

• is continuous at x = 0

• is differentiable at x = 0

• has a limit that exists at x = 0

• exists at x = 0

(Select All that Apply) The function shown

• is continuous at x = 0

• is differentiable at x = 0

• has a limit that exists at x = 0

• exists at x = 0

(Select all that apply) The function shown

• is continuous at x = 2

• is differentiable at x = 2

• has a limit that exists at x = 2

• exists at x = 2