5.2 Mean Value Theorem

5.2 Mean Value
Theorem

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Mean Value Theorem for Derivatives

Multiple Choice

a. Is the function satisfies the Mean Value Theorem(MVT)?

b. Find each value of c satisfy the MVT equation.

y=x²+2x-1 on [0,1]

• a. yes

  b. c= 1/2

• a. yes

  b. c=1

Multiple Choice

a. Is the function satisfies the Mean Value Theorem(MVT)?

b. Find each value of c satisfy the MVT equation.

y=x^1/3on [-1,1]

• a. yes

  b. c=3/2

• a. No

  b. none

Multiple Choice

a. Is the function satisfies the Mean Value Theorem(MVT)?

b. If no why?

$$f\left(x\right)=\sqrt[]{x^2}+1$$ on [-1,1]

• a.No

  b. discont. at x=0.5

• a. No

  b. not diff. at x=0. (corner)

Multiple Choice

a. Is the function satisfies the Mean Value Theorem(MVT)?

b. If no why?

$$f\left(x\right)=\left|x-1\right|$$ on [0,4]

• a.No

  b. not diff. at x=1 (corner)

• a. No

  b. not diff. at x=1.5. (cusp)

​​Increasing and Decreasing Functions

Multiple Choice

where is the functions $$y=x^2$$ increasing and where is it decreasing?

• $$\left(-\infty,0\right)$$ decrease

  $$\left(0,\infty\right)$$ increase

• $$\left(-\infty,\infty\right)$$ increase

Multiple Select

where is the functions $$y=x^3-4x$$ increasing and where is it decreasing?

• $$\left(-\infty,0\right)$$ decrease

• $$\left(-\infty,-\sqrt[]{\frac{4}{3\ }}\right]\ and\ \left[\sqrt[]{\frac{4}{3}},\infty\right]$$ increase

• $$\left[-\sqrt[]{\frac{4}{3}},\sqrt[]{\frac{4}{3}}\right]$$ decrease