Question on differentiation. (1 Viewer)

[theodore0307]

I need help with the following question:

Thanks.

 

[enigma_1]

<a href="http://www.codecogs.com/eqnedit.php?latex=f(1)=a(1)^2&plus;b(1)&plus;c" target="_blank"><img src="http://latex.codecogs.com/gif.latex?f(1)=a(1)^2&plus;b(1)&plus;c" title="f(1)=a(1)^2+b(1)+c" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=:.&space;a&plus;b&plus;c=5" target="_blank"><img src="http://latex.codecogs.com/gif.latex?:.&space;a&plus;b&plus;c=5" title=":. a+b+c=5" /></a> is your first equation


Now do the same thing by subbing in f'(1)=2, this will be your second equation.


For your third equation, sub in f"(1) = -1


Therefore you have 3 equations, and you can use simultaneous equations to solve them. The easiest way to start would be subbing in f"(1)=-1 because it's basically 2a=-1 therefore a=-0.5


And you sub that into wherever it can be subbed into. And proceed from there.

 

[tracyw]

f(1)= a(1)^2 + b(1) + c
= a+b+c
= 5
f'(1)= 2a(1)+b
= 2a+b
= 2
f''(1)= 2a
= -1

Thus, a = -0.5. 2a+b=2 so 2(-0.5)+b=2, so b=3. a+b+c=5 so, -0.5 + 3 + c = 5, so c= 2.5