Question

F:R—>R,f(x)=xeˣ,Determine intervals in which the given function are strictly increasing or strictly decreasing.

Answer 1

f : R –––>R , f(x) = xe^x

differentiate function, f(x) with respect to x,

f'(x) = xe^x + e^x = e^x(x + 1)

now, f'(x) = 0

e^x(x + 1) = 0 => x = -1

case 1 :- x > -1 , f'(x) < 0
so, function is strictly decreasing in (-1,∞)

case 2 :- x < -1 , f'(x) > 0
so, function is strictly increasing in (-∞, -1)

hence, function is strictly decreasing in (-1, ∞) while strictly increasing in (-∞, -1)

Answer 2

Dear student:

Given: R—>R,

f(x)=xeˣ

For determining the intervals in which f is increasing and decreasing.

Find derivative of f(x)

Then see the derivative in which f is positive and negative.

If it is positive then f is increasing

And if it is negative then f is decreasing.

See the attachment.