Suppose that f(0) = −5 and f '(x) ≤ 7 for all values of x. how large can f(5) possibly be?

f(5) cannot exceed 30.

Step-by-step explanation:

f is differentiable in all R, so we can apply the Mean Value Theorem on the interval [0,5], since f is continuous on [0,5] and differentiable on (0,5).

By the MVT, there exists some number c∈(0,5) such that . Substituting the value of f(0), this last equation is equivalent to . But f'(x)≤7 for all values of x, in particular for x=c, so applying this bound we obtain that . Then , so substracting 5 from both sides we conclude that .

$6.42

step-by-step explanation:

4

step-by-step explanation:

im pretty sure it's 4 beacsue 8/2 equals 4