Question

Giúp mình câu 75 với ạ

Answer 1

\(f'\left(x\right)=-2a.sin2x+b.cosbx\)

\(\Rightarrow\left\{{}\begin{matrix}f'\left(0\right)=-2a.sin\left(0\right)+b.cos\left(0\right)=2\\f'\left(\dfrac{\pi}{4}\right)=-2a.sin\left(\dfrac{\pi}{2}\right)+b.cos\left(\dfrac{b}{4}\right)=-4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}b=2\\-2a+2.cos\left(\dfrac{\pi}{2}\right)=-4\end{matrix}\right.\)

\(\Rightarrow a=b=2\)

\(\Rightarrow a^2+b^2=8\)