Question Number 104984 by mathocean1 last updated on 25/Jul/20
Commented by mathocean1 last updated on 25/Jul/20
![Here is the variation of f(x) in [−3;2]. the function g is such that ∀ x ∈[−3;2] , g′(x)=((f(x))/x^2 ). Choose the correct answer about the variation of g: a)g is non−decreasing in [−3;2] b)g is descending in [−3;2] c)g is monotonous in [−3;2] d) g is contant in [−3;2]. Please sirs detail...](Q104989.png)
$${Here}\:{is}\:{the}\:{variation}\:{of}\:{f}\left({x}\right)\:{in} \\ $$$$\left[−\mathrm{3};\mathrm{2}\right].\:{the}\:{function}\:{g}\:{is}\:{such}\:{that} \\ $$$$\forall\:{x}\:\in\left[−\mathrm{3};\mathrm{2}\right]\:,\:{g}'\left({x}\right)=\frac{{f}\left({x}\right)}{{x}^{\mathrm{2}} }. \\ $$$${Choose}\:{the}\:{correct}\:{answer}\:{about} \\ $$$${the}\:{variation}\:{of}\:{g}: \\ $$$$\left.{a}\right){g}\:{is}\:{non}−{decreasing}\:{in}\:\left[−\mathrm{3};\mathrm{2}\right] \\ $$$$\left.{b}\right){g}\:{is}\:{descending}\:{in}\:\left[−\mathrm{3};\mathrm{2}\right] \\ $$$$\left.{c}\right){g}\:{is}\:{monotonous}\:{in}\:\left[−\mathrm{3};\mathrm{2}\right] \\ $$$$\left.{d}\right)\:{g}\:{is}\:{contant}\:{in}\:\left[−\mathrm{3};\mathrm{2}\right]. \\ $$$$ \\ $$$$\mathcal{P}{lease}\:{sirs}\:{detail}... \\ $$