Question

Let f (X) = 2x^3-3x^2-12x+15 on {-2,4}. The relative maximum occurs at X=

Answer 1

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

Learn more:

examine the maxima and minima of the function f(x)=2x³-21x²+36x ...

https://brainly.in/question/1781825

find the local maximA or minima of the function: f(x)= sinx + cosx ...

https://brainly.in/question/21125629