Mathematics - Application of Derivative Question with Solution | TestHub

${\mathrm{f}}^1(\mathrm{x})=\frac{-5}{2}(1-\mathrm{x}{)}^{3/2}$ and ${\mathrm{f}}^{11}(\mathrm{x})=\frac{15}{4}(1-\mathrm{x}{)}^{1/2}$ and $\mathrm{f}(0)=1,{\mathrm{f}}^1(0)=\frac{-5}{2}$, ${\mathrm{f}}^{11}(\theta \mathrm{x})=\frac{15}{4}(1-\theta \mathrm{x}{)}^{1/2}$

Hence, $(1-x{)}^{5/2}=\frac{2-5x}{2}+\frac{x^2}{2}(1-\theta x{)}^{1/2}\times \frac{15}{4}$ as $x\to 1$, $0=1-\frac{5}{2}+\frac{15}{8}(1-\theta {)}^{1/2}\Rightarrow \theta =9/25$