Question

find the value of x...where there is possible relative max or min point (recall e^x is positive for all x). the 2nd derivative to determine the nature of the function

f(x) = (9+x) e ^ -4x

Answer 1

i take it this is \(f(x)=(9+x)e^{4-x}\)

did you take the first derivative?

Answer 2

Sorry it is supposed to be -4x

Answer 3

Using product rule, f'(x) = (x+9)* (-4)e^(-4x) + e^-4x = e^(-4x)*(-4(x+9) +1)) = e^(-4x)*(-4x-35)=-e^(4x)(4x+35)

Let f'(x) = 0
Using null factor law, x = -35/4

Sub that value into second derivative, if its f''(-35/4)>0, its a local min, if f''(-35/4) <0, its a local max, if f''(-35/4) = 0, its a stationary point of inflection.