Consider the function f (x) = 5x + 3x^-1. For this function there are four impor
ID: 2883958 • Letter: C
Question
Consider the function f (x) = 5x + 3x^-1. For this function there are four important intervals: (-infinity, A], [A, B) (B, C], and [C, infinity) where A, and C are the critical numbers and the function is not defined at B. Find A and B and C For each of the following intervals, tell whether f (x) is increasing (type in INC) or decreasing (type in DEC). (-infinity, A]: [A, B): (B, C]: [C, infinity) Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f (x) is concave up (type in CU) or concave down (type in CD). (-infinity, B): (B, infinity):Explanation / Answer
f(x) = 5x+ 3/x
to find the critical points
f'(x) = 0
=> 5 - 3/x^2 =0 => x = +/- sqrt(3/5)
i)
A = -sqrt(3/5)
B = 0
C = sqrt(3/5)
ii) in interval(-infinity , -sqrt(3/5] f(x) is increasing as the value increases
in interval[-sqrt(3/5,0) f(x) is increasing as the value increases
in interval(0, sqrt(3/5 ] f(x) is decreasing as the value decreases
in interval[sqrt(3/5 , infinity] f(x) is decreasing as the value decreases