Question

Find the interval in which y=x2e−x is increasing.

Answer 1

$\huge{\boxed{\mathtt{\red{ANSWER}}}}$ ----

The function e^(−x) is always positive,

so you only need to look at x(2−x).

Figure out on what interval it is positive.

It is positive if the two factors are both positive or both negative.

But the first factor is negative only if x<0, and on that interval (2−x) is positive.

Next, notice that (2−x) is positive precisely if x<2.

dy/dx = 2x*e^(−x)−x²e^(−x) = 0

⇒x=0,2

f(x) is increasing in [ 0 , 2 ]

in (−∞,0] ∪ [2, ∞) f(x) is decreasing.......

$<font color=red><marquee behaviour=alternate>_/\_мαяк ⓐⓢ вяαiηℓisт_/\_</marquee></font>$

$<font color=green><marquee behaviour=alternate>❤️Follow Me❤️</marquee></font>$