Question

The maximum value of function x³ - 15x² + 72x + 19 in the interval [1, 10] is ______.

Options

• 131

• 239

• 127

• None of these

Answer 1

The maximum value of function x³ - 15x² + 72x + 19 in the interval [1, 10] is 239.

Explanation:

Let f(x) = x³ - 15x² + 72x + 19

∴ f'(x) = 3x² - 30x + 72 = 0 at x = 4, 6

Again f"(x) = 6x - 30 is -ve at x = 4

So that f(4) = 131

At the end points, f(1) = 77, f(10) = 239

So that f(x) has its maximum value as 239.