So I've been doing this problem for a while now and I keep getting the wrong answer:
Find a cubic function, in the form below, that has a local maximum value of 4 at -4 and a local minimum value of 0 at 2.
So I just use can obtain 4 equations by subsituting (-4,4) and (2,0) into f(x) and into the derivative of f(x) where :
For f(x): at x=-4,
at x=2,
For f'(x): at x=-4,
at x=2,
So when I solve it I get a= -1/93, b= -1/31, c= 8/31, d= -28/93 but that only solves 3 of the above equations...so I'm doing something wrong. I'll post all my work in the next post since it's a bit long. Also, I don't know how to use matrices so try to refrain from using it. Thanks.
Step 1:
So input that into the rest:
Step 2:
Plug that into the the remaining two:
Step 3:
Then working back from there I got the rest I mentioned but it doesn't seem to work. Also, if you can get the answer in matrices I don't really mind but critique on this work would be preferred.
We haven't been taught matrices yet but my higher-year friend said that you can use it solve them. I'll learn it eventually but I'm technically not supposed to use matrices to solve this problem.
Wow, I sure did something wrong...Gah, better go check again.
Okay, I redid the whole question and finally got the answer the long way. I don't know why but I sure complicated myself...I should've just subtracted the similar ones from each other since that would've gotten rid of the "d"s in ones relative to f(x). Haha, I need to simplify more often. Anyways, thanks for all the help. I can't wait to learn matrices but that's actually going to happen in my data management class next semester. Bleh, such a long wait! =/