f(x)=${\sqrt{x^2+10x+34}}$
The answer choices are
A. -5,5
B. 0,-5
C. -5
D. 0,5
Using the chain rule I have found the derivative of this problem as
$(2x+10)$${1 \over2(x^2+10x+34)^1/2}$
Given that derivative when I plug in 0 to try and find the where the first derivative is equal to zero I end up with y=3
-5 is the only value where when I plug it in it seems to give me anything close to 3. Can anyone tell me if I am on the right track or what else I should try to do to solve this problem?
Your derivative seems to be correct, but then you get off track. Note that the fraction $\frac{2x+10}{2(x^2+10x+34)^{1/2}}$ is zero iff the numerator is zero. Thus you want to solve $2x+10=0$, which leads to $x=-5$. Also, be sure to check that the value found is in the domain of $f$ in the first place (it is).