IMathAS-libretexts

Find

\displaystyle {a}

and

\displaystyle {b}

such that

\displaystyle {f{{\left({x}\right)}}}={x}^{{2}}+{a}{x}+{b}

has an average value of

\displaystyle \frac{{40}}{{3}}

over [0,1] and an average value of

\displaystyle \frac{{28}}{{3}}

over [0,4].

\displaystyle {a}

\displaystyle {b}