JEE Main 2014Session, Shift 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002If fff and ggg are differentiable functions in [0,1]\left[ {0,1} \right][0,1] satisfying f(0)=2=g(1),g(0)=0f\left( 0 \right) = 2 = g\left( 1 \right),g\left( 0 \right) = 0f(0)=2=g(1),g(0)=0 and f(1)=6,f\left( 1 \right) = 6,f(1)=6, then for some c∈]0,1[c \in \left] {0,1} \right[c∈]0,1[AOption A. f′(c)=g′(c)f'\left( c \right) = g'\left( c \right)f′(c)=g′(c)BOption B. f′(c)=2g′(c)f'\left( c \right) = 2g'\left( c \right)f′(c)=2g′(c)COption C. 2f′(c)=g′(c)2f'\left( c \right) = g'\left( c \right)2f′(c)=g′(c)DOption D. 2f′(c)=3g′(c)2f'\left( c \right) = 3g'\left( c \right)2f′(c)=3g′(c)CheckSkip · show solution
