IIT-JEE 2010 · Paper 2 · Mathematics Q33

MathematicsSingle correct+3 / -1Question 33 of 57

Passage

Paragraph for Questions 31 to 33

Consider the polynomial $f(x)=1+2x+3x^2+4x^3.$ Let $s$ be the sum of all distinct real roots of $f(x)$ and let $t=|s|$ .

The function $f'(x)$ is

increasing in

\left(-t,-\dfrac14\right)

and decreasing in

\left(-\dfrac14,t\right)

decreasing in

\left(-t,-\dfrac14\right)

and increasing in

\left(-\dfrac14,t\right)

increasing in

(-t,t)

decreasing in

(-t,t)

Answer and worked solution

Official answer: B

Second derivative. $f''(x)=6+24x$ , negative for $x<-\frac14$ and positive for $x>-\frac14$ .

So $f'$ decreases on $\left(-t,-\frac14\right)$ and increases on $\left(-\frac14,t\right)$ (note $-t<-\frac12<-\frac14$ ).

(B)

Topics:Monotonicity

IIT-JEE 2010 · Paper 2, Mathematics question 33