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Category: Differentiation

given-that-f-x-mx-2-4-3-x-n-x-2-1-and-f-max-7-f-min-1-find-the-value-of-m-and-n-

Question Number 133179 by abdullahquwatan last updated on 19/Feb/21 $$\mathrm{given}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{mx}^{\mathrm{2}} +\mathrm{4}\sqrt{\mathrm{3}}\mathrm{x}+\mathrm{n}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{and}\:\mathrm{f}\:\mathrm{max}=\mathrm{7} \\ $$$$\mathrm{f}\:\mathrm{min}=−\mathrm{1}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{n} \\ $$ Commented by abdullahquwatan last updated on 20/Feb/21 $$\mathrm{thx} \\…

f-x-1-f-x-1-f-x-

Question Number 2071 by Rasheed Soomro last updated on 01/Nov/15 $$\left\{\:\left[{f}\left({x}\right)\right]^{−\mathrm{1}} \right\}'\:=\left[\:{f}\:'\left({x}\right)\:\right]^{−\mathrm{1}} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Yozzi last updated on 01/Nov/15 $$\frac{{d}}{{dx}}\left(\frac{\mathrm{1}}{{f}\left({x}\right)}\right)=\frac{\mathrm{1}}{{f}^{'} \left({x}\right)}…

If-f-x-and-g-x-have-no-constant-term-then-f-x-g-x-f-x-g-x-

Question Number 2005 by Rasheed Soomro last updated on 29/Oct/15 $${If}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{have}\:{no}\:{constant}\:{term}\:{then} \\ $$$${f}\:'\left({x}\right)={g}'\left({x}\right)\overset{?} {\:\Rightarrow\:}{f}\left({x}\right)={g}\left({x}\right)? \\ $$ Commented by prakash jain last updated on 30/Oct/15 $$\mathrm{If}\:{f}\left({x}\right)\neq{g}\left({x}\right)…

let-consider-a-function-g-defined-by-g-a-0-1-dx-1-x-1-ax-Give-the-defined-Domain-of-g-and-simplify-g-

Question Number 67465 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$ \\ $$$$\:\:{let}\:{consider}\:{a}\:{function}\:{g}\:{defined}\:{by}\:\:\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\:\sqrt{\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{ax}\right)}}\:\: \\ $$$${Give}\:{the}\:{defined}\:{Domain}\:{of}\:{g}\:\:{and}\:{simplify}\:{g}. \\ $$…