Let $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$ be defined by $f(x)=x^3+1$ Statement 1: The function fhas a local extremum at $x=0$ Statement 2: The function $f$ is continuous and differentiable on $(-\infty, \infty)$ and $f^{\prime}(0)=0$

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Aicharya · Accepted Answer

Let $f:(-\infty, \infty) ightarrow(-\infty, \infty)$ be defined by $f(x)=x^3+1$. Clearly, $f(x)$ is symmetric along $y=1$ and it has neither maxima nor minima. $	herefore$ Statement - 1 is false.

Let $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$ be defined by $f(x)=x^3+1$ Statement 1: The function…

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