HW #22 (3.1-3.2 review)

Differentiate y= x³ + 2x

• 3x³+2x
• 3x²+2
• 3x+2
• 3x

find 

• y = 2 x^-1
• y=2 x^-2
• y= −2x^-2
• y= −2 x^-1

Tags

CCSS.HSF-IF.C.7A

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

Find the derivative of the given equation
f(x) = -4x

• 4
• x
• -4
• 0

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

Is the function is the following graph differentiable at x = 0? Why?

• Yes. The limit from the left and right of 0 both approach 0.

• No, $\lim_{x\rightarrow0}\left|x\right|\$ does not exist.

• No, $\lim_{h\rightarrow0}\frac{\left(\left|x+h\right|-\left|x\right|\right)}{h}$ does not exist.

• Yes, the function is differentiable because there is a constant rate of change of -1 from $\left(-\infty,0\right)$ and 1 from $\left(0,\infty\right)$ .

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