# Thread: f'(x) compared to g'(x) inequality problem

1. ## f'(x) compared to g'(x) inequality problem

Assume f is differentiable for all x. The signs of f' are as follows.
f'(x) {greater than sign} 0 on (-infinity,-40
f'(x) {less than sign} 0 on (-4,6)
f'(x) {greater than sign} 0 on (6, infinity)

Supply the appropriate inequality for the indicated value of c. (The sign goes inbetween the { marks)
Function
g(x)=f(x)+5

Sign of g'(c)
g'(0) { } 0

I think this question might involve moving the graph. If I take f(x) and move it up five....at least I think I should move it up five... will the derivative still have the same sign? Any ideas of what to do are greatly appreciated. Thanks for your help!!

2. Originally Posted by liz155
Assume f is differentiable for all x. The signs of f' are as follows.
f'(x) {greater than sign} 0 on (-infinity,-40
f'(x) {less than sign} 0 on (-4,6)
f'(x) {greater than sign} 0 on (6, infinity)

Supply the appropriate inequality for the indicated value of c. (The sign goes inbetween the { marks)
Function
g(x)=f(x)+5

Sign of g'(c)
g'(0) { } 0

I think this question might involve moving the graph. If I take f(x) and move it up five....at least I think I should move it up five... will the derivative still have the same sign? Any ideas of what to do are greatly appreciated. Thanks for your help!!
Since g(x)=f(x)+5, g'(x)=f'(x), and so:

g'(x) > 0 on (-infinity,-4)
g'(x) < 0 on (-4,6)
g'(x) > 0 on (6, infinity)

so g'(0)<0

RonL

3. Thanks for you help. I see what you did.

--Cori