Question

Let f(x) = 2x3 - 3x2 - 12x + 15 on (-2,4). The relative
maximum occurs at x =​

Answer 1

Answer:

Step-by-step explanation:

1

Answer 2

Given :  f(x) = 2x³ - 3x² - 12x + 15  on (-2 ,  4)  

To Find : relative maximum occurs at x=

Solution:

f(x) = 2x³ - 3x² - 12x + 15  

=> f'(x)  = 6x²  - 6x - 12

f'(x)   = 0

=> 6x²  - 6x - 12 = 0

=> x² -  x - 2 = 0

=> x²  - 2x + x - 2 = 0

=> x(x - 2) + 1(x - 2) = 0

=> (x + 1)(x - 2) = 0

=> x = - 1 , x = 2

-1 & 2 both lies in (-2 ,  4)  

f''(x)  = 12x  - 6

f'(-1)  = 12(-1) - 6 = - 18 < 0

Hence relative maxima occurs here

f''(2) = 12(2) - 6 = 18 >0

Hence relative minima occurs here

relative maximum occurs at X=   - 1

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