Mathematics - Application of Derivative Question with Solution | TestHub

(A) $f(x)=(x-1{)}^2(x-2{)}^5$ $f^{\prime }(x)=(x-1{)}^2(x+2{)}^4(8x+1)$ 1 point of minima at $\mathrm{x}=-\frac{1}{8}$ $f^{\prime \prime }(x)=0\text{ for }x=1,-2$ Two points of inflection (B)$f(x)=3\sin x+4\cos x-5x$ $f^{\prime }(x)=3\cos x-4\sin x-5\le 0$ $f^{\prime \prime }(x)=-3\sin x-4\cos x=0$for infinite value of x (C)

$\mathrm{x}=1$point of maxima as well as point of inflection (D)${\mathrm{f}}^{\prime }(\mathrm{x})=\frac{3}{5}(\mathrm{x}-1{)}^{-2/5}\ge 0\forall \mathrm{x}\in \mathrm{R}$ $f^{\prime \prime }(x)=\frac{-3}{5}\times \frac{2}{5}(x-1{)}^{-7/5}$ which changes sign at $\mathrm{x}=1$ $\mathrm{x}=1$ point of inflection