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 ]

Engineering

Mathematics

Lagranges Mean Value Theorem

Question

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)

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

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

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

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Let h(x) = f (x) – 2g(x)

Apply Rolle's theorem to h(x) in [0, 1].