Consider the function f(x) 7x + 9x-1. For this function there are four important
ID: 2884967 • Letter: C
Question
Consider the function f(x) 7x + 9x-1. For this function there are four important intervals: ( - oo, A], [A, B), (B, Cl, and [C, oo) where A, and C are the critical numbers and the function is not defined at B Preview Preview Preview Find A and B and C For each of the following open intervals, tell whether f(x) is increasing or decreasing (-oo, A): Select an answer (A, B): Select an answer (B, C): Select an answer (C, oo) Select an answer 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 or concave down (oo, B): Select an answer B, oo): Select an answerExplanation / Answer
f(x) = 7x + 9x-1
f '(x) = 7 -9x-2
Critical points, f '(x)=0
7-9x-2=0
x = +-3 / sqrt 7
So the intervals are (-inf, -3/sqrt7) , (-3/sqrt7, 0), (0 , 3/sqrt7), (3/sqrt 7, infinity)
Therefore A= -3/sqrt 7 , B =0, C =3/sqrt 7
In (-inf,-3/sqrt7), f '(x)>0
In (-3/sqrt7,0), f '(x)<0
In (0,3 sqrt 7, f'(x) <0
In (3/sqrt 7, inf), f'(x)>0
f ''(x) = -9(-2)x-3=18x-3
So the intervals are (-inf,0),(0,inf)
Therefore B =0
In (-inf,0), f ''(x)<0
In (0,inf), f ''(x)>0
So in (-inf,B), concave down
In (B, inf), concave up