Question-214163

Question Number 214163 by issac last updated on 29/Nov/24

Commented by mathkun last updated on 30/Nov/24

I am a begginer in Calculus. How do you find the derivative of this function? The equation for y with respect to x is not given.

$$\mathrm{I}\:\mathrm{am}\:\mathrm{a}\:\mathrm{begginer}\:\mathrm{in}\:\mathrm{Calculus}. \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{this}\:\mathrm{function}? \\ $$$$\mathrm{The}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{y}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{x}\:\mathrm{is}\:\mathrm{not}\:\mathrm{given}. \\ $$

Commented by issac last updated on 30/Nov/24

:) it is nonsense to find the derivative of that function ((dy(t))/dt) Because function y(t) is not clearly specified however we can find the point of ((dy(t))/dt)=0 the meaning of the differantial coefficient 0 is because it can regarded as the maximum/minimum value of function pls find wikipedia documents Maximum and Minimum

$$\left.\::\right) \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{nonsense}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{derivative} \\ $$$$\mathrm{of}\:\mathrm{that}\:\mathrm{function}\:\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\:\mathrm{Because}\: \\ $$$$\mathrm{function}\:{y}\left({t}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{clearly}\:\mathrm{specified} \\ $$$$\mathrm{however}\:\mathrm{we}\:\mathrm{can}\:\mathrm{find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\: \\ $$$$\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}=\mathrm{0}\:\:\mathrm{the}\:\mathrm{meaning}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{differantial}\:\mathrm{coefficient}\:\mathrm{0}\:\mathrm{is}\:\mathrm{because} \\ $$$$\mathrm{it}\:\mathrm{can}\:\mathrm{regarded}\:\mathrm{as}\:\mathrm{the}\:\mathrm{maximum}/\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{function}\:\mathrm{pls}\:\mathrm{find}\:\mathrm{wikipedia} \\ $$$$\mathrm{documents}\:\mathrm{Maximum}\:\mathrm{and}\:\mathrm{Minimum} \\ $$

Commented by issac last updated on 30/Nov/24

and Quiz i′ve created is about inflection point which are also where we can find the point where the Shape of a function change from a concave function to a convex function without having to differantial twice

$$\mathrm{and}\:\mathrm{Quiz}\:\mathrm{i}'\mathrm{ve}\:\mathrm{created}\:\mathrm{is}\:\mathrm{about} \\ $$$$\mathrm{inflection}\:\mathrm{point}\:\mathrm{which}\:\mathrm{are}\:\mathrm{also}\:\mathrm{where} \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{where}\:\mathrm{the} \\ $$$$\mathrm{Shape}\:\mathrm{of}\:\mathrm{a}\:\mathrm{function}\:\mathrm{change}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{concave}\:\mathrm{function}\:\mathrm{to}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{function} \\ $$$$\mathrm{without}\:\mathrm{having}\:\mathrm{to}\:\mathrm{differantial}\:\mathrm{twice} \\ $$

Answered by issac last updated on 29/Nov/24

additional problem! f;R^1 →R^1 , f∈C^n at t∈(−∞,∞) (f is n time differantiable function) find inflection point of f(t) where intervel t∈(0,∞) Do you want try it?? :)

$$\mathrm{additional}\:\mathrm{problem}! \\ $$$${f};\mathbb{R}^{\mathrm{1}} \rightarrow\mathbb{R}^{\mathrm{1}} \:,\:{f}\in\boldsymbol{\mathcal{C}}^{{n}} \:\mathrm{at}\:{t}\in\left(−\infty,\infty\right)\: \\ $$$$\left({f}\:\mathrm{is}\:{n}\:\mathrm{time}\:\mathrm{differantiable}\:\mathrm{function}\right) \\ $$$$\mathrm{find}\:\mathrm{inflection}\:\mathrm{point}\:\mathrm{of}\:\:{f}\left({t}\right) \\ $$$$\mathrm{where}\:\mathrm{intervel}\:{t}\in\left(\mathrm{0},\infty\right)\: \\ $$$$\left.\mathrm{Do}\:\mathrm{you}\:\mathrm{want}\:\mathrm{try}\:\mathrm{it}??\::\right) \\ $$

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