Let f: , ( - , ) ( - , ) be defined by f(x) = x^3 + 1. Statement … - Vidyadip

MCQ

Let $f:\,\left( { - \infty ,\infty } \right) \to \left( { - \infty ,\infty } \right)$ be defined by $f(x) = x^3 + 1$.

Statement $1$ : The function $f$ has a local extremum at $x = 0$

Statement $2$ : The function $f$ is continuous and differentiable on $\left( { - \infty ,\infty } \right)$ and $f'(0) = 0$

A
Statement $1$ is true, Statement $2$ is false.
B
Statement $1$ is true, Statement $2$ is true, Statement $2$ is a correct explanation for Statement $1$
C
Statement $1$ is true, Statement $2$ is true, Statement $2$ is not the correct explanation for Statement $1$
✓
Statement $1$ is false, Statement $2$ is true.

✓

Answer

Correct option: D.

Statement $1$ is false, Statement $2$ is true.

d
Let $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$ be defined by

$f(x)=x^{3}+1$.

Clearly, $f(x)$ is symmetric along $y=1$ and

it has neither maxima nor minima.

$\therefore$ Statement $-1$ is false.

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