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 161802 by femKaren last updated on 22/Dec/21

Answered by mr W last updated on 22/Dec/21

$$f\left(x\right)={\cos }^{3}x+{\sin }^{3}x$$$$f^{\prime }\left(x\right)=-3{\cos }^{2}x\sin x+3{\sin }^{2}x\cos x$$$$=3\cos x\sin x(\sin x-\cos x)=0$$$$forx\in (0,\frac{\pi }{2}):\cos x\ne 0,\sin x\ne 0$$$$therefore$$$$\sin x-\cos x=0$$$$\Rightarrow \tan x=1\Rightarrow x=\frac{\pi }{4}\Rightarrow \cos x=\sin x=\frac{\sqrt{2}}{2}$$$$f{\left(x\right)}_{extremum}=2\times {\left(\frac{\sqrt{2}}{2}\right)}^3=\frac{\sqrt{2}}{2}$$

Commented by femKaren last updated on 22/Dec/21

$$thankyousomuch!$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com