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Question Number 156188 by naka3546 last updated on 09/Oct/21

$$Givenarationalfunction$$$$f\left(x\right)=\frac{{ax}^2+bx+c}{x+q}$$$$hasminimumpointat(-2,9)andmaximumpointat(2,1).$$$$Findvalueofa,b,c,andq.$$

Commented by MJS_new last updated on 09/Oct/21

$$\mathrm{we}\mathrm{have}4\mathrm{unknowns}\mathrm{and}\mathrm{need}4\mathrm{equations}$$$$\left(1\right)f(-2)=9$$$$\left(2\right)f\left(2\right)=1$$$$\left(3\right)f^{\prime }(-2)=0$$$$\left(4\right)f^{\prime }\left(2\right)=0$$$$\mathrm{solve}\mathrm{this}\mathrm{to}\mathrm{get}$$$$a=-1$$$$b=5$$$$c=-4$$$$q=0$$

Commented by naka3546 last updated on 09/Oct/21

$$Thankyou,sir.$$

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