Can someone help me please ? Suppose f(x) is continuous on [2,7] and −2≤f′(x)≤4 for all x in (2,7). Use the Mean Value Theorem to estimate f(7)−f(2).

Question

Suppose f(x) is continuous on [2,7] and −2≤f′(x)≤4 for all x in (2,7). Use the Mean Value Theorem to estimate f(7)−f(2).

answer = [..............] ≤f(7)−f(2)≤ [.............]

Answer 1

Hello Mo! The Mean Value Theorem, provided that the function is continous and differentiable, states that: ( f(7) - f(2) ) / ( 7 - 2 ) = f ' (c), where 2 < c < 7.

Rearrange the equation by multiplying 5 by both sides so that 5 * f ' (c) = f(7) - f(2).

We know that the smallest derivative is -2 and that 5 * ( - 2 ) = -10

We also know that the largest derivative is 7 and that 5 * 7 = 35

The difference between f(7) and f(2) must be ⇒ -10 ≤ f(7) - f(2) ≤ 35 >>>>>>>> (ANSWER)

Hope this helps!