Question

What is the largest possible value of f(0), where f(x) is continuous and differentiable on the interval [-5, 0], such that f(-5)= 8  and f'(c)≤2.

(a) 2

(b) -2

(c) 18

(d) -18

The question was asked in an interview.

I would like to ask this question from Cauchy’s  Mean Value Theorem in portion Differential Calculus of Engineering Mathematics

Answer 1

Right option is (b) -2

The best I can explain: From the Mean Value Theorem, we have, \(f'(c) = \frac{f(b)-f(a)}{b-a} \)

\(f'(c) = \frac{f(0)-f(-5)}{-5-0} \)

-5f’ (c) = f(0)-8

f(0)=8 – 5f'(c) ≤ 8-5(2) = -2

 f(0)=-2