91Ó°ÊÓ

\(\operatorname{If} f(x)=\left\\{\begin{array}{ll}2 x^{2}+\frac{2}{x^{2}}, & 0<|x| \leq 2 \\ 3, & x>2\end{array}\right.\), then (a) \(x=1,-1\) are the points of global minima (b) \(x=1,-1\) are the points of local minima (c) \(x=0\) is the points of local minima (d) None of the above

Let \(f(x)\) be a polynomial with real coefficients satisfies \(f(x)=f^{\prime}(x) \times f^{\prime \prime \prime}(x)\). If \(f(x)=0\) satisfies \(x=1,2,3\) only, then the value of \(f^{\prime}(1) \times f^{\prime}(2) \times f^{\prime}(3)\) is equal to (a) positive (b) negative (c) 0 (d) inadequate data

Let \(f(x)=\frac{x-1}{x^{2}}\), then which of the following is correct? (a) \(f(x)\) has minima but no maxima. (b) \(f(x)\) increases in the interval \((0,2)\) and decreases in the interval \((-\infty, 0) \cup(2, \infty)\) (c) \(f(x)\) can come down in \((-\infty, 0) \cup(0,3)\) (d) \(x=3\) is the point of inflection

Consider the function \(f(x)=\frac{x^{2}}{x^{2}-1}\) \(f\) has (a) local maxima but not local minima (b) local minima but not local maxima (c) both local maxima and local minima (d) neither local maxima nor local minima