The function f(x) = 2x3 - 15x2 + 36x + 4 is maximum at x = 1. 3 2… - Vidyadip

Question

The function f(x) = 2x³- 15x² + 36x + 4 is maximum at x =

3
0
4
2

✓

Answer

2

Soluctio :

Given, f(x) = 2x³- 15x² + 36x + 4

lmplies that f'(x) = 6x²- 30x + 36

For a local maxima or a local minima, we must have f'(x) = 0

lmplies that 6x² - 30x + 36 = 0

lmplies that x² - 5x + 6 = 0

(x - 2)(x - 3) = 0

lmplies that x = 2, 3

Now, f''(x) = 12x - 30

lmplies that f''(2) = 24 - 30 = 6 < 0

Therefore, x = 1 is a local maxima.

Also, f''(3) = 36 - 30 = 6 > 0

Therefore, x = 2 is a local maxima.

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