Question

Verify Mean Value Theorem, if f (x) = x³ – 5x² – 3x in the interval [a, b], where a = 1 and b = 3. Find all c ∈ (1, 3) for which f ′(c) = 0.

Answer 1

The given function f is f (x) = x³ – 5x² – 3x

f, being a polynomial function, is continuous in [1, 3] and is differentiable in (1, 3) whose derivative is 3x² − 10x − 3.