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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES2 Marks
Question
Find the absolute maximum value and the absolute minimum value of the following function in the given intervals:
$\text{f}\text{(x)}=\text{x}^3, \text{x}\in[-2, 2]$
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Answer

Given: $\text{f}\text{(x)} =\text{x}^3, \text{x}\in [-2,\ 2]\ \Rightarrow\ \ \text{f}'\text{(x)}=3\text{x}^2$
$\text{Now }\text{f}\text{'(x)} =0\ \Rightarrow\ \ 3\text{x}^2=0\ \Rightarrow\ \ \text{x}=0\in[-2,\ 2]$
At $x = 0,$ $f(0) = 0$
At $x = -2,$ $f(-2) = (-2)^3 = -8$
At $x = 2,$ $f(2) = (2)^3 = 8$
Therefore, absolute minimum value of $f(x)$ is $-8$ and absolute maximum value is $8.$

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