Consider the equation below. f(x)=e^6x+e^-x

Question

Consider the function below. f(x)=e^6x+e^-x

(a) Find the intervals on which f is increasing. (Enter your answer using interval notation.)

Ans: (-ln(6)/7,infinity)

Find the interval on which f is decreasing. (Enter your answer using interval notation.)

Ans: (-infinity,-ln(6)/7)

(b) Find the local minimum value of f.

Ans:________

Answer 1

desmos.com/calculator/ztqyyxnhe4

Answer 2

This function has one minimum point at (1/7) ln (1/6) which is approximately -.25; you find this value by setting the first derivative equal to 0 and solving for x.

To the left of this minimum the function is decreasing and to the right increasing.