Consider the function f(x) = 5x^3 +5x^2 + 7, and let c be a number in the interval [0.1] . For what values of k is there a c in this interval such that ?
______≤k≤______
f(0) = 7
f(1) = 17
7 ≤ k ≤ 17 for 0 ≤ c ≤1
It might be necessary to look at relative maxima and minima within the interval to prove that f(x) does not cover a wider range. f(x) increases monotonically in the interval, so the answer should be correct.