Question

If f(x) = 3x³ - 9x² - 27x + 15, then the maximum value of f(x) is _______.

Options

• - 66

• 30

• - 30

• 66

Answer 1

If f(x) = 3x³ - 9x² - 27x + 15, then the maximum value of f(x) is 30.

Explanation:

We have,

f(x) = 3x³ - 9x² - 27x + 15

⇒ f'(x) = 9x² - 18x - 27

For maxima or minima, we put f'(x) = 0

⇒ 9x² - 18x - 27 = 0

⇒ x² - 2x - 3 = 0

⇒ (x - 3)(x + 1) = 0

⇒ x = -1, 3

Now, f''(x) = 18x - 18

at x = - 1, f'' (x) = 18(- 1) - 18 = - 36 < 0

So, x = - 1, point of maxima

∴ Maximum value of f(x) at x = - 1 is

f(- 1) = 3(-1)³ - 9(- 1)² - 27(-1) + 15

= - 3 - 9 + 27 + 15

= - 12 + 42

= 30