Supposef(0) = 2 and 2 ≤ f '(x) ≤ 7for all x in the interval [−5, 5]. determine the greatest and least possible values of f(2).least

If the slope of the function is 2, the amount it can change over the interval 0–2 is

... 2×2 = 4 units

If the slope is 7, the amount it can change over the interval 0–2 is

... 2×7 = 14 units

The least possible value of f(2) is 2+4 = 6.

The greatest possible value of f(2) is 2+14 = 16.

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