Which of the following is an increasing funct | vedclass

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(B) To determine if a function $f(x)$ is increasing,we check its derivative $f'(x)$. If $f'(x) > 0$ for all $x$ in the domain,the function is strictly

Vedclass · Accepted Answer

$e^{x^3}$

Vedclass · Answer

(B) To determine if a function $f(x)$ is increasing,we check its derivative $f'(x)$. If $f'(x) > 0$ for all $x$ in the domain,the function is strictly increasing.$1$. For $f(x) = e^{x^2}$,$f'(x) = e^{x^2} \cdot 2x$. This is positive for $x > 0$ and negative for $x $2$. For $f(x) = e^{x^3}$,$f'(x) = e^{x^3} \cdot 3x^2$. Since $e^{x^3} > 0$ and $3x^2 \ge 0$ for all $x$,$f'(x) \ge 0$. The function is strictly increasing on $\mathbb{R}$.$3$. For $f(x) = e^0 = 1$,$f'(x) = 0$. This is a constant function,not strictly increasing.Therefore,$e^{x^3}$ is the correct choice as it is an increasing function.

Which of the following is an increasing function?

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