Mathematics - Application of Derivative Question with Solution | TestHub

$f(x)$ is periodic of period 1 Consider $x\in [0,1)$ $f^{\prime }(x)=2\pi \cos 2\pi x+1$ $f^{\prime }(x)=0$ if $x=\alpha ,\beta$ where $\frac{1}{4}<\alpha <\frac{1}{3}<\frac{1}{2}<\beta <\frac{3}{4}$ $f^{\prime }(x)>0\text{ if }x\in [0,\alpha )\text{ or }(\beta ,1)$ $f^{\prime }(x)<0$ if $x\in (\alpha ,\beta )$ $f(0)=f(1)=0;f(\alpha )>0$ $f$ has local maxima at $\alpha$.