3.2 Differentiability

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

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

Where is the graph 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

CCSS.HSA.REI.D.10

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

• True
• False