Suppose f(x) is continuous on [3,6] and −3≤f′(x)≤5 for all x in (3,6). Use the Mean Value Theorem to estimate f(6)−f(3).

  -9  ≤ f(6) - f(3)  ≤ 15

Step-by-step explanation:

In order to use the Mean Value Theorem, it must be continuous and differentiable. Both of these conditions are satisfied so we can continue.  

Find f(6) - f(3) using the following formula:

Consider:    a = 3, b = 6

Given: -3 ≤  f'(x)  ≤ 5

          -9  ≤ 3f'(c) ≤ 15    Multiplied each side by 3

→   -9  ≤ f(6) - f(3)  ≤ 15  Substituted 3f'(c) with f(6) - f(3)

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step-by-step explanation:

answer: the answer is   graph (a)