If f(x)=4 x^8, then : - Vidyadip

MCQ

If $f(x)=4 x^8$, then :

A
$\text{f}\ '\Big(\frac{1}{2}\Big)=\text{f}'\Big(-\frac{1}{2}\Big)$
B
$\text{f}\Big(\frac{1}{2}\Big)=-\text{f}'\Big(-\frac{1}{2}\Big)$
✓
$\text{f}\Big(-\frac{1}{2}\Big)=\text{f}\Big(-\frac{1}{2}\Big)$
D
$\text{f}\Big(\frac{1}{2}\Big)=\text{f}'\Big(-\frac{1}{2}\Big)$

✓

Answer

Correct option: C.

$\text{f}\Big(-\frac{1}{2}\Big)=\text{f}\Big(-\frac{1}{2}\Big)$

$f(x)=4 x^8,$
$\Rightarrow\text{f}\Big(\frac{1}{2}\Big)=4\Big(\frac{1}{2}\Big)^8=\frac{4}{256}=\frac{1}{64}$
$\Rightarrow\text{f}\Big(-\frac{1}{2}\Big)=4\Big(-\frac{1}{2}\Big)^8=\frac{4}{256}=\frac{1}{64}$
$\Rightarrow\text{f}\Big(-\frac{1}{2}\Big)=\text{f}\Big(-\frac{1}{2}\Big)$

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