JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q72

MathematicsSingle correct+4 / -1Question 72 of 90

If Rolle's theorem holds for the function $f(x)=2x^3+bx^2+cx$ , $x\in[-1,1]$ , at the point $x=\dfrac12$ , then $2b+c$ equals :

−1

−3

Answer and worked solution

Official answer: B

Rolle: $f(-1)=f(1)$ gives $-2+b-c=2+b+c$ , so $c=-2$ . Also $f'(\frac12)=\frac32+b+c=0$ , so $b=\frac12$ . Then $2b+c=-1$ .

JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 72