Question

If function $f\left(x\right)=\lambda \sin x+\cos x$ has two extremum points in $[0,2\pi ],$ then the value of $\lambda$ can be

• A. $-\frac{3}{13}$
• B. $0$
• C. $\frac{2}{7}$
• D. $1$

Answer 1

Answer: (A), (C), (D)

$1$

Given : $f\left(x\right)=\lambda \sin x+\cos x$
$\Rightarrow f^{\prime }\left(x\right)=\lambda \cos x-\sin x$
for critical points : $f^{\prime }\left(x\right)=0$
$\Rightarrow \lambda \cos x-\sin x=0\Rightarrow \tan x=\lambda$
Plotting the graph :
Clearly, for $\lambda >0$ or $\lambda <0$, we get two solutions
but for $\lambda =0$ gives three solutions