Question

The function f(x) =2x^3-9x^2+100 is maximum at​

Answer 1

Answer:

Explanation:

f(x) = 2x3 - x2 - 4x – 4

f’(x) = 6x2 - 2x – 4

As f’(x) = 0

Implies 6x2 - 2x – 4 = 0

3x – x – 2 = 0 (By dividing by 2)

(3x – 2)(x + 1) = 0

3x – 2 = 0 implies x = -2/3

Or x + 1 = 0 implies x = -1

f’(x) = 6x2 - 2x – 4

f’’(x) = 12x – 2

At max point f’’(x) < 0

∴f’’(x) = 12x – 2 at x = -1

= 12(-1) – 2

= -12 – 2 = -14

∴Max at x = 1