Given \[f\text{ }\left( x \right)\text{ }=\text{ }sin\text{ }2x\] Differentiate w.r.t x, we get \[f'\left( x \right)\text{ }=\text{ }2\text{ }cos\text{ }2x,\text{ }0\text{ }<\text{ }x\text{...
Given, $f(x)=x^{3}-6 x^{2}+9 x+15$ Differentiate with respect to $x$, we get, $f^{\prime}(x)=3 x^{2}-12 x+9=3\left(x^{2}-4 x+3\right)$ $=3(x-3)(x-1)$ For all maxima and minima, $ \begin{array}{l}...
As per the given question, Therefore \[x\text{ }=\text{ }0,\] now for the values close to \[x\text{ }=\text{ }0,\] and to the left of \[0,\text{ }f'\left( x \right)\text{ }>\text{ }0\] Also for...
Differentiate with respect to $x$, we get, $ \begin{array}{l} f(x)=(x+2)^{2}+2(x-1)(x+2) \\ =(x+2)(x+2+2 x-2) \\ =(x+2)(3 x) \end{array} $ For all maxima and minima, $ \begin{array}{l} f(x)=0 \\...
Given, $f(x)=x^{2}(x-1)^{2}$ Differentiate with respect to $x$, we get, $ \begin{array}{l} {\left x=3 x^{2}(x-1)^{2}+2 x^{2}(x-1)\right.} \\ =[x-1]\left(3 x^{2}(x-1)+2 x^{2}\right) \\ =[x-1]\left(3...
Given, $f(x)=x^{2}-3 x$ Differentiate with respect to $x$ then we get, $ f(x)=3 x^{2}-3 $ $\mathrm{Now}, \mathrm{f}(x)=0$ $ 3 x^{2}=3 \Rightarrow x=\pm 1 $ Again differentiate $f(x)=3 x^{2}-3$ $...
Given $f(x)=(x-5)^{4}$ Differentiate with respect to $x$ $ f(x)=4(x-5)^{2} $ For local maxima and minima $ \begin{array}{l} f(x)=0 \\ =4(x-5)^{2}=0 \\ =x-5=0 \\ x=5 \end{array} $ $f(x)$ changes from...