Cho hàm số f(x)= asin x + bcos x + 1

* Hướng dẫn giải

Ta có: \({f^/}\left( x \right) = a\cos x - b\sin x\).

Do \(\left\{ \begin{array}{l}{f^/}\left( 0 \right) = \frac{1}{2}\\f\left( { - \frac{\pi }{4}} \right) = 1\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}a = \frac{1}{2}\\ - \frac{{\sqrt 2 }}{2}a + \frac{{\sqrt 2 }}{2}b + 1 = 1\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}b = \frac{1}{2}\\a = \frac{1}{2}\end{array} \right.\).