Question

Let $f : \left(-\infty, \infty\right) \to \left(-\infty , \infty \right)$ be defined by $f(x) = x^3 + 1$. The function f has a local extremum at $x = 0$ The function f is continuous and differentiable on (-??,oo) and/'(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.
• D. Statement 1 is false, Statement 2 is true.

Answer 1

Answer: (D)

Statement 1 is false, Statement 2 is true.

Answer 2

$f : \left(-\infty, \infty\right) \to \left(-\infty , \infty \right)$ be defined by $f\left(x\right) = x^{3} + 1$. Clearly, $f\left(x\right)$ is symmetric along $y = 1$ and it has neither maxima nor minima. $\therefore$ Statement - 1 is false.