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 132785 by liberty last updated on 16/Feb/21

Commented by liberty last updated on 16/Feb/21

$$\mathrm{y}={\mathrm{ax}}^4+{\mathrm{bx}}^3+{\mathrm{cx}}^2+\mathrm{dx}+\mathrm{e}$$

Answered by MJS_new last updated on 16/Feb/21

$$‘‘\mathrm{critical}{\mathrm{point}}^{″}\mathrm{means}\min /\max ?\mathrm{in}\mathrm{this}\mathrm{case}:$$$$p\left(x\right)={ax}^4+{bx}^3+{cx}^2+dx+e$$$$p^{\prime }\left(x\right)=4{ax}^3+3{bx}^2+2cx+d$$$$p^{″}\left(x\right)=12{ax}^2+6bx+2c$$$$\mathrm{we}\mathrm{need}5\mathrm{equations}$$$$\left(1\right)p\left(0\right)=3\left[(0\mid 3)\mathrm{on}\mathrm{curve}\right]$$$$\left(2\right)p^{\prime }\left(0\right)=0\left[\min /\max \right]$$$$\left(3\right)p\left(1\right)=2\left[(1\mid 2)\mathrm{on}\mathrm{curve}\right]$$$$\left(4\right)p^{″}\left(1\right)=0\left[\mathrm{inflection}\right]$$$$\left(5\right)p^{\prime }\left(1\right)=-6\left[\mathrm{slope}\mathrm{of}\mathrm{tangent}\right]$$$$\mathrm{now}\mathrm{solve}\mathrm{the}\mathrm{system}\mathrm{for}a,b,c,d,e$$

Commented by liberty last updated on 16/Feb/21

$$\mathrm{i}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{understand}\mathrm{inflectional}$$$$\mathrm{tangent}$$

Commented by MJS_new last updated on 16/Feb/21

$$\mathrm{the}\mathrm{tangent}\mathrm{is}6x+y=8\iff y=-6x+8$$$$\mathrm{slope}\mathrm{is}-6$$$$\mathrm{I}\mathrm{corrected}\mathrm{it}$$

Commented by malwan last updated on 16/Feb/21

$$Ifound$$$$e=3,d=0,a=9,b=-22,c=12$$

Commented by liberty last updated on 16/Feb/21

$$\mathrm{thank}\mathrm{you}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com