Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 77024 by Sathvik last updated on 02/Jan/20

$$\mathrm{The}\mathrm{possible}\mathrm{value}\mathrm{of}\mathrm{p}\mathrm{for}\mathrm{which}$$$$\mathrm{graph}\mathrm{of}\mathrm{the}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)={2\mathrm{p}}^2-$$$$3\mathrm{ptan}\mathrm{x}+\tan {}^2\mathrm{x}+1\mathrm{does}\mathrm{not}\mathrm{lie}\mathrm{below}$$$$\mathrm{x}-\mathrm{axis}\mathrm{for}\mathrm{all}\mathrm{x}\in (\frac{-\mathrm{\Pi }}{2},\frac{\mathrm{\Pi }}{2})\mathrm{is}$$$$\left(\mathrm{a}\right)0\left(\mathrm{b}\right)4\left(\mathrm{c}\right)3\left(\mathrm{d}\right)8$$

Answered by MJS last updated on 03/Jan/20

$$\mathrm{well},\mathrm{just}\mathrm{test}\mathrm{them}\mathrm{all}...$$$$\mathrm{I}\mathrm{found}-2⩽p⩽2$$$$\Rightarrow \left(a\right)\mathrm{is}\mathrm{the}\mathrm{right}\mathrm{answer}$$$$f\left(x\right):y={\tan }^{2}x-3p\tan x+2p^2+1$$$$f^{\prime }\left(x\right):y={2\tan }^{3}x-3p{\tan }^{2}x+2\tan x-3p=$$$$=({\tan }^{2}x+1)(2\tan x-3p)$$$$\Rightarrow \tan x=\frac{3}{2}p$$$$\mathrm{insert}\mathrm{in}f\left(x\right)$$$$y=1-\frac{p^2}{4}=0\Rightarrow p=\pm 2$$$$\Rightarrow -2⩽p⩽2$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com