GATE Electrical 2012 | Question: 27

Question

The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is

• A. $21$
• B. $25$
• C. $41$
• D. $46$

Answer 1

f'(x)=3x^2-18x+24=0

x^2-6x+8=0

x=4,2

f(2)=8-36+48+5=25

f(4)=64-144+96+5=21

so B

Comments

I think you are not checking at the endpoint ... f(6) =41 ...so answer will be option C... 

Reason : f(x) is polynomial function ,it is both continous and differenciable ..if u check the nature of first derivatives of f(x) ...it will convex ..it means maximum we will find at endpoint ....

Answer 2

correct Answer : option C.. { hint: check at endpoint}