f'(x) compared to g'(x) inequality problem

• Sep 15th 2007, 06:13 PM
liz155
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!! :)
• Sep 16th 2007, 12:26 AM
CaptainBlack
Quote:

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
• Sep 16th 2007, 01:01 PM
liz155
Thanks for you help. I see what you did.:)

--Cori