Let f be any continuous function on [0,2] and twice differentiable on (0,2). If f(0)=0,f(a)=1 and f(b)=2, then

Question

Accepted Answer

Correct answer: B. (b) f(0) = 0 f(a) = 1 and f(b) = 2 Let h(x) = f(x) – x has three roots By Rolle’s theorem h′(x) = f ′(x) – 1 has at least two roots h′′(x) = f ′′(x) = 0 has at least one roots

$Let f be any continuous function on [0,2] and twice differentiable on (0,2). If f(0)=0,f(a)=1 and f(b)=2, then$

Solution

More Continuity & Differentiability PYQs