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Category: Differentiation

f-x-x-3-27x-Find-intervals-where-given-fuction-ii-is-1-increasing-2-decreasing-3-concave-up-and-down-4-point-of-inflection-

Question Number 77294 by Rabnawaz last updated on 05/Jan/20 $${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{27}{x} \\ $$$${Find}\:{intervals}\:{where}\:{given}\:{fuction}\:{ii} \\ $$$${is} \\ $$$$\mathrm{1}.{increasing} \\ $$$$\mathrm{2}.{decreasing} \\ $$$$\mathrm{3}\:{concave}\:{up}\:{and}\:{down} \\ $$$$\mathrm{4}\:{point}\:{of}\:{inflection} \\ $$…

given-the-function-y-1-x-2-1-The-tangent-equation-of-the-curve-with-the-smallest-gradient-is-

Question Number 77271 by jagoll last updated on 05/Jan/20 $$\mathrm{given}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}.\:\mathrm{The}\:\mathrm{tangent}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{with}\:\mathrm{the}\:\mathrm{smallest}\: \\ $$$$\mathrm{gradient}\:\mathrm{is}\:.. \\ $$ Terms of Service Privacy Policy Contact:…

discrete-mathematics-prove-that-n-1-1-F-2n-1-1-5-5-2-F-n-fibonacci-sequence-

Question Number 142723 by mnjuly1970 last updated on 04/Jun/21 $$\:\:\:\:\:\:\:\:…….\:{discrete}\:\:…..\:\:{mathematics}……. \\ $$$$\:\:\:\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{F}_{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1}}\overset{?} {=}\frac{\mathrm{5}−\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:{F}_{{n}} \:::\:{fibonacci}\:\:{sequence}… \\ $$ Answered by…

A-geometric-sequence-with-n-terms-a-1-a-2-a-3-a-n-which-has-a-1-a-n-3-If-the-product-of-all-n-terms-a-1-a-2-a-3-a-n-59049-Determine-the-value-of-n-

Question Number 11633 by Joel576 last updated on 29/Mar/17 $$\mathrm{A}\:\mathrm{geometric}\:\mathrm{sequence}\:\mathrm{with}\:{n}\:\mathrm{terms}\: \\ $$$${a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:…,\:{a}_{{n}} \:\mathrm{which}\:\mathrm{has}\:{a}_{\mathrm{1}} \:.\:{a}_{{n}} \:=\:\mathrm{3} \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:{n}\:\mathrm{terms}\:=\:{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}} …{a}_{{n}} =\:\mathrm{59049} \\…

Prove-that-n-N-k-1-n-1-sin-kpi-2n-k-1-n-1-cos-kpi-2n-

Question Number 142698 by Willson last updated on 04/Jun/21 $$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\:\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\prod}}\mathrm{sin}\left(\frac{\mathrm{k}\pi}{\mathrm{2n}}\right)\:=\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\prod}}\mathrm{cos}\left(\frac{\mathrm{k}\pi}{\mathrm{2n}}\right) \\ $$ Answered by Ar Brandon last updated on…