JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q72

MathematicsSingle correct+4 / -1Question 72 of 90

If $f$ and $g$ are differentiable functions in $[0,1]$ satisfying $f(0)=2=g(1)$ , $g(0)=0$ and $f(1)=6$ , then for some $c\in\,]0,1[$ :

f'(c)=g'(c)

f'(c)=2g'(c)

2f'(c)=g'(c)

2f'(c)=3g'(c)

Answer and worked solution

Official answer: B

Let $h=f-2g$ . Then $h(0)=2-0=2$ and $h(1)=6-2\cdot2=2$ . By Rolle's theorem $h'(c)=0$ for some $c\in(0,1)$ , i.e. $f'(c)=2g'(c)$ .

JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 72