# Suppose that 4≤𝑓′(𝑥)≤6 for all values of 𝑥. Use the Mean Value Theorem to find values for the inequality below.?

a≤𝑓(2)−𝑓(−2)≤b

### 2 Answers

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- SlowfingerLv 61 month ago
According to mean value theorem,

min f '(x) ≤ (f(x1) - f(x2))/(x1-x2) ≤ max f '(x)

min f '(x) = 4

max f '(x) = 6

Let x1=2 and x2=-2

4 ≤ (f(2) - f(-2))/(2+2) ≤ 6

4 ≤ (f(2) - f(-2))/4 ≤ 6

multiply by 4

16 ≤ f(2) - f(-2) ≤ 24

a=16

b=24

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