Let denote the set of all real numbers. Let f : → be defined by f(x)= array cl 6 x+ x 2…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let 
denote the set of all real numbers. Let f : → be defined by \[f(x)=\left\{\begin{array}{cl}
\frac{6 x+\sin x}{2 x+\sin x} & \ ext { if } x \
eq 0, \\
\frac{7}{3} & \ ext { if } x=0 .
\end{array}\right.\]Then which of the following statements is (are) TRUE?
denote the set of all real numbers. Let f : → be defined by \[f(x)=\left\{\begin{array}{cl}
\frac{6 x+\sin x}{2 x+\sin x} & \ ext { if } x \
eq 0, \\
\frac{7}{3} & \ ext { if } x=0 .
\end{array}\right.\]Then which of the following statements is (are) TRUE?- The point x = 0 is a point of local maxima of f
- The point x = 0 is a point of local minima of f
- Number of points of local maxima of f in the interval [p, 6p] is 3
- Number of points of local minima of f in the interval [2p, 4p] is 1
Answer
(D) Number of points of local minima of f in the interval [2 p , 4 p ] is 1
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