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Question Number 13075 by Joel577 last updated on 13/May/17

$$S\left(x\right)\mathrm{is}\mathrm{the}\mathrm{sum}\mathrm{of}49\mathrm{terms}\mathrm{of}\mathrm{AP}$$$$\mathrm{The}\mathrm{first}\mathrm{term}\mathrm{is}\frac{1}{2}{x}^3\mathrm{and}\mathrm{the}\mathrm{difference}$$$$\mathrm{is}(7-x)$$$$\mathrm{If}S\left(x\right)\mathrm{maximum},\mathrm{the}\mathrm{value}\mathrm{of}{10}^{\mathrm{th}}\mathrm{term}\mathrm{is}...$$

Commented by ajfour last updated on 13/May/17

$$localmaximum?x=-4then,$$$$T_{10}=\frac{{(-4)}^3}{2}+9[7-(-4)]$$$$=-32+99=67.$$

Commented by Joel577 last updated on 13/May/17

$$\mathrm{How}\mathrm{did}\mathrm{u}\mathrm{get}x=-4?$$

Commented by ajfour last updated on 13/May/17

$$S\left(x\right)=\frac{49}{2}\{2\left(\frac{x^3}{2}\right)+48(7-x)\}$$$$\frac{dS}{dx}=\frac{49}{2}\{3x^2-48\}=0$$$$\Rightarrow x^2=16$$$$x=\pm 4.$$

Commented by ajfour last updated on 13/May/17

Commented by Joel577 last updated on 13/May/17

$$thankyouverymuch$$

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