Question

Let F(x) = f(x) g(x) h(x) ∀ real x, where f(x), g(x) and h(x) are differentiable functions. At same point x₀, F'(x₀) = 21F(x₀), f'(x₀) = 4 f(x₀), g'(x₀) =-7g(x₀) and h'(x₀) = kh(x₀),then k =......

Answer 1

Given, F(x) = f(x) g(x) h(x)

On differentiating at x = x₀, we get

On substituting in Eq. (i). we get