AP EAMCET · Maths · Differentiation
If \(f(x)=\sqrt{x+\sin x}\), then all the points of the set \(\left\{(x, f(x)) / f^{\prime}(x)=0\right\}\) lie on
- A a circle
- B a straight line
- C an ellipse
- D a parabola
Answer & Solution
Correct Answer
(D) a parabola
Step-by-step Solution
Detailed explanation
\(f(x)=\sqrt{x+\sin x}\) (given)...(1) Since \(f^{\prime}(x)=0\) \[ \begin{aligned} & \Rightarrow \frac{(1+\cos x)}{2 \sqrt{x+\sin x}}=0 \\ & \Rightarrow \cos x=-1 \\ & \Rightarrow x=(2 n+1) \pi, n \in \mathbb{Z} \end{aligned} \] at \(x=(2 n+1) \pi\),…
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