JEE Math Practice Question
If $$f$$ and $$g$$ are differentiable functions in $$\left[ {0,1} \right]$$ satisfying $$f\left( 0 \right) = 2 = g\left( 1 \right),g\left( 0 \right) = 0$$ and $$f\left( 1 \right) = 6,$$ then for some $$c \in \left] {0,1} \right[$$
- A.$$f'\left( c \right) = g'\left( c \right)$$
- B.$$f'\left( c \right) = 2g'\left( c \right)$$
- C.$$2f'\left( c \right) = g'\left( c \right)$$
- D.$$2f'\left( c \right) = 3g'\left( c \right)$$
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