Question

F (x) = - eˣ Baseline (x - 4)
What​ is(are) the critical​ point(s) of​ f?

Answer 1

given,

`f(x) = (-e^x)/(x - 4)`

to find the critical point of the given expression

fist differentiating the function

`f'(x) = -((x-4)e^x+ e^x)/((x - 4)^2)`

`f'(x) = (-(x-4)e^x- e^x)/((x - 4)^2)`

`f'(x) = (-e^x(x-3))/((x - 4)^2)`

now equating differential equation to zero

`(e^x(-x+3))/((x - 4)^2)=0`

`e^x(-x+3)=0`

now,

-x + 3 = 0 and eˣ ≠ 0

x = 3

the critical number will be equal to x = 3

`y = (-e^3)/(3 - 4)`

`y =e^3`