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 170566 by cortano1 last updated on 27/May/22

$$\mathrm{Find}\min \mathrm{value}$$$$f\left(x\right)=(x+4)(x+5)(x+6)(x+7)$$

Answered by som(math1967) last updated on 27/May/22

$$(x+4)(x+7)(x+5)(x+6)$$$$(x^2+11x+28)(x^2+11x+30)$$$$(a+28)(a+30)[leta=x^2+11x]$$$$a^2+58a+840$$$${(a+29)}^2-{29}^2+840$$$${(a+29)}^2-1$$$${(a+29)}^2⩾0$$$${(a+29)}^2-1⩾-1$$$$\therefore (x+4)(x+5)(x+6)(x+7)⩾-1$$$$\therefore minvalueoff\left(x\right)is-1$$

Answered by ajfour last updated on 27/May/22

$$letx+\frac{11}{2}=t$$$$f\left(t\right)=(t-\frac{3}{2})(t-\frac{1}{2})(t+\frac{1}{2})(t+\frac{3}{2})$$$$=(t^2-\frac{9}{4})(t^2-\frac{1}{4})$$$$let{t}^2-\frac{5}{4}=z$$$$f\left(z\right)=z^2-1$$$$f\left(z\right){\mid }_{min}=-1$$$$whent=x+\frac{11}{2}=\pm \frac{\sqrt{5}}{2}$$$$x=\frac{-11\pm \sqrt{5}}{2}$$

Commented by Tawa11 last updated on 08/Oct/22

$$\mathrm{Great}\mathrm{sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com