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!! :)

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

Thanks for you help. I see what you did.:)

--Cori