Let f∈C1(a,b)f \in C^1(a,b)f∈C1(a,b), limx→a+f(x)=+∞\lim\limits_{x \to a+} f(x) = +\inftyx→a+limf(x)=+∞, limx→b−f(x)=−∞\lim\limits_{x \to b-} f(x) = -\inftyx→b−limf(x)=−∞ and f′(x)+f2(x)≥−1f'(x) + f^2(x) \ge -1f′(x)+f2(x)≥−1 for x∈(a,b)x \in (a,b)x∈(a,b). Prove that b−a≥πb - a \ge \pib−a≥π and give an example where b−a=πb - a = \pib−a=π.
Hidden so you can work on the problem first.