Question

$1.Thefunction{x}^5-5x^4+5x^3-10hasamaximawhenxis$

Answer 1

Dear student
Que 6
$$\begin{gathered} \mathrm{I}=\int \left(\sin 4\mathrm{t}+2\mathrm{t}\right)\mathrm{dt} \\ =-\frac{\cos 4\mathrm{t}}{4}+\frac{2{\mathrm{t}}^2}{2}+\mathrm{C} \\ =-\frac{\cos 4\mathrm{t}}{4}+{\mathrm{t}}^2+\mathrm{C} \\ \mathrm{Note}:\int \sin 4\mathrm{t}\mathrm{dt} \\ \mathrm{Take}4\mathrm{t}=\mathrm{u}\Rightarrow \mathrm{dt}=\frac{1}{4}\mathrm{du} \\ \mathrm{So},\int \sin 4\mathrm{t}\mathrm{dt}=\frac{1}{4}\int \mathrm{sinu}\mathrm{du}=-\frac{1}{4}\mathrm{cosu}=-\frac{1}{4}\cos 4\mathrm{t} \end{gathered}$$
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