Question

The absolute maximum and minimum values of the function \[ f(x)=\sin x+\sqrt3\cos x,\quad x\in[0,\pi] \] are:

• A. Minimum value \(=\dfrac1{\sqrt3}\), maximum value \(=2\)
• B. Minimum value \(=-\sqrt3\), maximum value \(=2\)
• C. Minimum value \(=\sqrt3\), maximum value \(=2\)
• D. Minimum value \(=-\dfrac1{\sqrt3}\), maximum value \(=2\)

Hint:

Convert expressions of the form \[ a\sin x+b\cos x \] into \[ R\sin(x+\alpha) \] to easily determine extrema.

Answer 1

The Correct Option is B