微积分intervalConsider the equation below.(Round the answers to three decimal places.If you need to use - or ,enter -INFINITY or INFINITY.) f(x) = e^3x + e^-x (a) Find the interval on which f is increasing.Find the interval on which f is decreasing.(b) Find the local minimum value of f.(c) Find the interval on which f is concave up.
问题描述：
微积分interval
Consider the equation below.(Round the answers to three decimal places.If you need to use - or ,enter -INFINITY or INFINITY.)
f(x) = e^3x + e^-x
(a) Find the interval on which f is increasing.
Find the interval on which f is decreasing.
(b) Find the local minimum value of f.
(c) Find the interval on which f is concave up.
答
(a) Take the derivative of f(x)f'(x)=3e^3x - e^-x > 03e^3x > e^-xe^-x (3e^4x-1) >0e^4x > 1/34x> -ln3x> -1/4 ln 3(-1/4 ln 3, Infinity) f is increasing(negative infinity, -1/4 ln 3) f is monotonically d...