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MathCraft: PDF to LaTeX file: Sample-02

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rightarrow \mathbb{R}$ is convex, then $$ f\left(\frac{a+b}{2}\right) \leqslant \frac{1}{b-a} \int_{a}^{b} f(x) d x \leqslant \frac{f(a)+f(b)}{2} . $$ \noindent\textbf{Proof}: First of all,... rapfigure} \vspace{.2 in} Let now $r(x)=f\left(\frac{a+b}{2}\right)+c\left(x-\frac{a+b}{2}\right)$ be