Question

Consider the function f(x)=e^x/6+e^x. Compute the derivative of this function.

f′(x) = [6e^x/(6+e^x)^2]


a.) f(x) is increasing on the interval : ?

b.) f(x) is decreasing on the interval : na

c.) f(x) has a local minimum at : na

d.) f(x) has a local maximum at : na

e.) f′′(x) = 6e^x*(6-e^x)/(e^x+6)^3

f.) f(x) is concave up on the interval: (-inf,ln6)

g.) f(x) is concave down on the interval : (ln6,inf)

h.) f(x) has a point of inflection at : log(2)+log(3)

Can someone please help me finish this? I don't know what the increasing interval is...

Answer 1

f(x) is increasing whenever f'(x) is positive. That derivative appears to be positive everywhere.