Question

If f(x) is differentiable in [a, b] such that f(1) = 2, f(2) = 6, then there exists at least one c, a < c < b such that (b³ – a³) f '(3) =

• A. c²
• B. 2c²
• C. –3c²
• D. 12c²

Answer 1

Let f(x) = f(x) + Ax³ and choose A such that f(1) = f(2) ̃ A = $\frac{- f(b) + f(a)}{b^{3} - a^{3}}$

since f(x) satisfies condition of Rolle's theorem

f'(3) = 0 for some c Î (a, b)