Math help?

Yusuke Urameshi

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I know this doesn't belong on this site, but why not ask, right? If any of you guys know how to solve this, help would be greatly appreciated. The prof. never taught us how to do this. If you could explain how you got what you did so I can understand it in the future, that'd be awesome. Thanks, guys!

2. If f(x)=ax^2+b, f(−5)=6 and f′(−5)=2, find the coefficients a and b.
 
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flamefletcher

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allright
First Put x=-5 in ax^2+b.
We get 25a+b=6. This is Equation 1.
Now Differentiate f(x). that is what f`(x) means.
we get 2ax.Now put x=-5 and we get -10a=2
So a=-1/5. Put in equation one and solve to get b.
b is 11
Ans a=-1/5,b=11
 
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htitanf5

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f'(x) = 2ax (using chain rule, I found the derivative)
Since f'(-5) = 2, You substitute it in to find (a)
f'(-5)= 2a(-5) ---> -10a
Since it gave us that f'(-5)= 2 you can sub it in
so 2= -10a so (a)= -1/5

I think you can solve for (b) from there...
I'm a bit new to Calc but I think this is right...
 
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Yusuke Urameshi

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f'(x)=2ax
f'(-5)=-10a=2
a=-1/5
f(-5)=-1/5*25+b=-5+b=6
b=11

Don't you have the book with you? It can't be a lecture-only class, is it?
The book is pretty much only useful for the formulas and such. It doesn't have an example of anything like this. And the book only has real-world story problems, which doesn't really help in one's understanding in a mathematical process.

There's lectures on Monday, Wednesday, and Friday and then online homework. I don't really care for the setup.
 

Hexuze

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The book is pretty much only useful for the formulas and such. It doesn't have an example of anything like this. And the book only has real-world story problems, which doesn't really help in one's understanding in a mathematical process.

There's lectures on Monday, Wednesday, and Friday and then online homework. I don't really care for the setup.
Use youtube for help? One awesome math channel is:
 

Agent Phrank

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The book is pretty much only useful for the formulas and such. It doesn't have an example of anything like this. And the book only has real-world story problems, which doesn't really help in one's understanding in a mathematical process.

There's lectures on Monday, Wednesday, and Friday and then online homework. I don't really care for the setup.
Well then, I guess you can always rely on NB to solve your science/math problems :D
 

Funky Tiger

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I know this doesn't belong on this site, but why not ask, right? If any of you guys know how to solve this, help would be greatly appreciated. The prof. never taught us how to do this. If you could explain how you got what you did so I can understand it in the future, that'd be awesome. Thanks, guys!

2. If f(x)=ax^2+b, f(−5)=6 and f′(−5)=2, find the coefficients a and b.
Dude, its p easy.
f(-5) = 2. which means 25a + b = 2.

also, let y=f(x)
so y = ax[sup]2[/sup] + b
so x=((y-b)/a)[sup]½[/sup]
so f′(x) = ((x-b)/a)[sup]½[/sup]

so 4a = -5-b
or 4a + b = -5


Solve the two equations
 
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