Let $f(x)=2 x^{3}-24 x+107$ $ \therefore f^{\prime}(x)=6 x^{2}-24=6\left(x^{2}-4\right) $ Now, for local maxima and local minima we have $f^{\prime}(x)=0$ $ \begin{array}{l} \Rightarrow...

(ii) Solution: (i) Given function is $f(x)=3 x^{4}-8 x^{3}+12 x^{2}-48 x+25$ on $[0,3]$ On differentiating we get $ \begin{array}{l} f^{\prime}(x)=12 x^{3}-24 x^{2}+24 x-48 \\...

(i) (ii) Given function is \[f\left( x \right)\text{ }=~{{\left( x\text{ }-\text{ }1 \right)}^{2}}~+\text{ }3\] On differentiation we get \[\Rightarrow \text{ }f'\left( x \right)~=\text{ }2\left(...