Question

Verify Mean Value Theorem, if f (x) x² -4x-3 in the interval [a,b] where a =1 and b =4

Answer 1

The given function is f (x) = x²-4x-3

f, being a polynomial function, is continuous in [1, 4] and is differentiable in (1, 4) whose derivative is 2x − 4.

Mean Value Theorem states that there is a point c∈ (1, 4) such that f'( c) =1

Hence, Mean Value Theorem is verified for the given function.