Question

Find all relative extrema of the function. (If an answer does not exist, enter DNE.)
f(x) = x^2 + 2x + 14

Answer 1

"extrema" as in minima and maxima?

Answer 2

If so, take the first derivative and set it equal to zero.

Find all the solutions (values of x where this is true). With the original function, determine whether these points are minima or maxima by taking points just before and just after.

Answer 3

so if I take the first derivative it would be f'=2x+2
and then setting it to zero would look like f'=2x+2=0, then if x=-1 it would then equal 0. So would I then take the limit as it approaches x at -1 for f(-1)=x(-1)^2+2(-1)+14?

Answer 4

im not sure if this is what the question is askin for, is it this?

Answer 5

I'm not sure what extrema is.. let me see what else i can find out...

Answer 6

This is what it looks like

Answer 7

oh okay, yeah thats what it is http://en.wikipedia.org/wiki/Maxima_and_minima

Answer 8

it looks like it is asking for 4 points

Answer 9

would I then put -1, 0 and then 0, -1?

Answer 10

no, thats not right. I'm not sure, look at the graph http://www.wolframalpha.com/input/?i=x%5E2%2B2x%2B14

Answer 11

theres only 1 minimum, the maxima at both ends is infinity

Answer 12

soo looking at the link it says global minimum is -1? I'm not sure how to input it for (x,y). That means x=-1 and y=0 right? and then the maxima would be 0,inf?

Answer 13

it would be ( -1, f(-1) )

f(-1) is what you found above

Answer 14

then maxima \(\pm \infty\), not sure how you're supposed to format it

Answer 15

no, i dont open word files from the internet.

Answer 16

sure, or you can post it as a pdf, which would be quicker

Answer 17

relative maximum DNE

relative min: (-1, 13)

Answer 18

so there is no maximum? and for the bottom two i just had to solve for it? that isn't so bad. :)

Answer 19

it's not eh! :) the main point of this is to take the derivative and find where f'(x)=0, those are the "turning points" of the graph, where the slope is horizontal. Then determine whether those points are maxima or minima.

Answer 20

oh ok! Thank you for explaining it to me. I hope it sticks long enough to take my next test! :)

Answer 21

haha write it down! :P but no problem!