Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 205825 by tri26112004 last updated on 31/Mar/24

$${\left[f^{\prime }\left(x\right)\right]}^2+4f\left(x\right)=8x^2-32x+28$$$$\Rightarrow f\left(x\right)=¿$$

Commented by mr W last updated on 31/Mar/24

$$f\left(x\right)=x^2-4x+3$$$$or$$$$f\left(x\right)=-2x^2+8x-9$$$$or...$$

Answered by MM42 last updated on 31/Mar/24

$$f={ax}^2+bx+c\Rightarrow f^{\prime }=2ax+b$$$$\Rightarrow 4a^2{x}^2+4abx+b^2+4{ax}^2+4bx+4c=8x^2-32x+28$$$$\Rightarrow 4a^2+4a=8\Rightarrow a=1ora=-2$$$$4ab+4b=-32\mathrm{\&}{b}^2+4c=28$$$$ifa=1\Rightarrow b=-4\mathrm{\&}c=3$$$$\Rightarrow f\left(x\right)=x^2-4x+3✓$$$$ifa=-2\Rightarrow b=8\mathrm{\&}c=-9$$$$\Rightarrow f\left(x\right)=-2x^2+8x-9✓$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com