Question

The absolute maximum values of f(x) = x
3 − 3x
2 + 12 on the closed interval [-2, 4] occurs at x =

a. 4
b. 2
c. 1
d. 0
e. -2

Answer 1

KISSAN EKTA ZINDABAD

(e).-2

Answer 2

Function

Given:

Function f(x) is given as $x^3-3x^2+12$.

The range is given as [-2,4].

To find:

The maximum value of this function in this closed range.

Explanation:

In these type of question , it is needed to check at the boundary value, then it can be found out by analyzing the value the function at both boundary range.

So, first we will find out the value of f(x) at  -2

$f(-2)=(-2)^3-3(-2)^2+12=-8-12+12\\\\\implies f(-2)=-8$

The value of f(x) at 4

$f(4)=(4)^3-3(4)^2+12=64-48+12\\\\\implies f(4)=28$

As it can be seen this function is increasing in nature , so the maximum value of this function in given closed range is at x=4.