Given,

\(f(x)=4-7x^{4}\)

\(\Rightarrow f'(x)=0-7 \cdot 4x^{3}=-28x^{3}\)

Now f'(x)=0

\(\Rightarrow -28x^{3}=0\Rightarrow x=0\)

Step 2

Therefore absolute maximum value occurs at \(x = 0\) and absolute maximum value is,

\(f(0)=4-7(0)^{4}=4\)

Hence absolute maximum value is 4 and this occurs at \(x = 0\).