IIT-JEE 2009 · Paper 2 · Mathematics Q31

MathematicsInteger+4 / -1Question 31 of 57

The maximum value of the function $f(x)=2x^3-15x^2+36x-48$ on the set $A=\left\{x\mid x^2+20\le9x\right\}$ is

Your answer

Answer and worked solution

Official answer: 7

The set. $x^2-9x+20\le0$ gives $4\le x\le5$ .

Monotone. $f'(x)=6(x-2)(x-3)>0$ there, so the maximum is at $x=5$ :
$f(5)=250-375+180-48=7.$

Answer: 7

IIT-JEE 2009 · Paper 2, Mathematics question 31