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 171762 by pete last updated on 20/Jun/22

$$\mathrm{The}\mathrm{curve}\mathrm{for}\mathrm{which}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{a}(\mathrm{x}-\mathrm{p})(\mathrm{x}-\mathrm{q}),$$$$\mathrm{where}\mathrm{a},\mathrm{p}\mathrm{and}\mathrm{q}\mathrm{are}\mathrm{constants},\mathrm{has}\mathrm{turning}$$$$\mathrm{points}\mathrm{at}(2,0)\mathrm{and}(1,1).$$$$\mathrm{i})\mathrm{state}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{p}\mathrm{and}\mathrm{q}.$$$$\mathrm{ii})\mathrm{using}\mathrm{these}\mathrm{values},\mathrm{determine}\mathrm{the}\mathrm{value}$$$$\mathrm{of}a$$

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

$$a(x-p)(x-q)=0$$$$\Rightarrow x=p,q$$$$\Rightarrow p=1,q=2$$$$\frac{dy}{dx}=a(x-1)(x-2)=a(x^2-3x+2)$$$$y=a(\frac{x^3}{3}-\frac{3x^2}{2}+2x)+C$$$$0=a(\frac{8}{3}-\frac{3\times 4}{2}+2\times 2)+C$$$$1=a(\frac{1}{3}-\frac{3}{2}+2)+C$$$$\Rightarrow a=6,C=-4$$

Commented by pete last updated on 21/Jun/22

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com