Question

What is the relative max/min of g’(x) = (x + 4)eˣ

Answer 1

Hi there! :)

`\large\boxed{\text{Relative minimum at x = -4}}`

`g'(x) = (x + 4)e^(x)`

Find the critical point by setting g'(x) to 0:

`0 = (x + 4)e^(x)`

Set each factor equal to 0:

`0 = x + 4\\\\-4 = x\\\\0 \\eq e^(x)`

Therefore, the only critical point is at x = -4. Test to see whether this is a relative min or max by plugging in values on both sides into the equation for g'(x):

`g'(-5) = (-5 + 4)e^(-5) = -0.0067, -`

`g'(-3) = (-3 + 4)e^(-3) = 0.0498, +`

The graph changes from - to + at x = -4, so there is a relative minimum at x = -4.