Question

The function f(x) = x(x + 3)e^{- x/2} satisfies all the conditions of Rolle’s theorem on [-3, 0].

Find the value of c such that f'(c) = 0.

Answer 1

The function f(x) satisfies all the conditions of Rolle’s theorem, therefore there exist c ∈ (-3, 0) such that f'(c) = 0.

Hence, c = -2.