$**$Do not copy any OpenAl or solution manual. If you do & you can't answer my follow up question, that is cheating.

Consider the function in the given interval. $f(x)=2sinx-sin2x$;$[0,]$

a$.$ Sketch the graph of the function, including local max$/$min and inflection point $($if exist$).$ The inflection point may not be a special angle, then round the inflection point $($both $x$ and $y$ coordinates$)$ to one decimal.

b$.$ Find the average value $(f_{\text{a}\text{v}\text{e}})$ of the function, and draw a horizontal line $y=f_{\text{a}\text{v}\text{e}}$ to the graph of $f(x).$

Find the number $b$ such that the average value of $f(x)=2+6x-3x^2$ on the interval $0,b$ is $-1.$