hard problem dealing with local min and local max and concave up concave down?

Question

Suppose that f(x) = 7 - 4 e^x.

(A) List all the critical values of f(x).

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D) List the x values of all local maxima of f(x).
x values of local maximums =

(E) List the x values of all local minima of f(x).
x values of local minimums =

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values of all the inflection points of f.
x values of inflection points =

Answer 1

f(x) = 7 - 4e^x

f '(x) = - 4e^x always negative

f is a decreasing function
no maximum, no minimum

f ''(x) = -4e^x

f is concave down
no inflexion point