Question and Answers Forum

All Questions      Topic List

Differentiation Questions

Previous in All Question      Next in All Question      

Previous in Differentiation      Next in Differentiation      

Question Number 169826 by cortano1 last updated on 10/May/22

$$Givenf\left(x\right)=\sqrt{\sin x}+\sqrt{3\cos x}$$$$x\in (0,\frac{\pi }{2})$$$$Findmaxf\left(x\right).$$

Answered by mr W last updated on 10/May/22

$$f^{\prime }\left(x\right)=\frac{\cos x}{2\sqrt{\sin x}}-\frac{3\sin x}{2\sqrt{3\cos x}}=0$$$${\left(\tan x\right)}^{\frac{3}{2}}=\frac{1}{\sqrt{3}}$$$$\Rightarrow \tan x=\frac{1}{\sqrt[3]{3}}$$$$\sin x=\frac{1}{\sqrt{1+\sqrt[3]{9}}},\cos x=\frac{\sqrt[3]{3}}{\sqrt{1+\sqrt[3]{9}}}$$$$f{\left(x\right)}_{max}=\frac{1+\sqrt[3]{9}}{\sqrt[4]{1+\sqrt[3]{9}}}={(1+\sqrt[3]{9})}^{\frac{3}{4}}✓$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com