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Applications of Derivatives — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsApplications of Derivatives1 Mark
Question
Show that the function $f(x)=x^3+10 x+7$ for $x \in \mathrm{R}$ is strictly increasing.
✓

Answer

Given that $f(x)=x^3+10 x+7$
Differentiate w. r. t. $x$.
$
f^{\prime}(x)=3 x^2+10
$
Here, $3 x^2 \geq 0$ for all $x \in \mathrm{R}$ and $10>0$.
$
\therefore 3 x^2+10>0 \Rightarrow f^{\prime}(x)>0
$
Thus $f(x)$ is a strictly increasing function.

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