Differentiability and Four Theorems

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).

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

• x = -1

• x = 0

• x = 2

• x = 3; x = -2

True or False: Continuity implies differentiability 

• True
• False

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

• True

• False

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

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.C.7B

For the function shown in graph, which of the following is not true.

• is continuous at x = b

• is differentiable at x = b

• has a limit that exists at x = b

• exists at x = b

Where is the function shown in the graph not differentiable?

• x = -2, -1, 0, 1

• x = -2, -1, 1

• x = -2, -1

• x = -1, 0

 $f\left(x\right)=x^3+2x,\ \ \ \left[-1,1\right]$  


Find the value of c guaranteed by the Mean Value Theorem.

• 1/√3

• -1/√3

• ±1/√3

• The MVT doesn't apply