Quick question about slope and finding f(x)

f(x) := ax˛ + bx + c

find a, b, c ∈ R so that:

for x=-1 f(x)=0, the slope at this point is 2

and for x=1 f'(x)=0

what i haven't encountered before is the expression, THE SLOPE AT THIS POINT IS 2. Does that mean that i take the derivative of the first equation f(x) and that for x=-1 f'(-1)=2, so -2a+b=2 ??

the other two points are clear to me, a-b+c=0 and 2a+b=0

Re: Quick question about slope and finding f(x)

It has been very clearly mentioned that slope at x=-1 is 2, so you have $\displaystyle f'(-1)=2$.

That means $\displaystyle b-2a=2$.

Solve the following equations to get the value of a,b and c.

$\displaystyle \begin{cases} a-b+c=0 \\ b-2a=2 \\ 2a+b=0 \end{cases}$

Re: Quick question about slope and finding f(x)

I know that but my qeustion was (maybe i didn't make it very clear..) when we know the VALUE of the SLOPE in a certain point X, does it translate to>> derivative f'(x) = value of slope, at that point?? Do i take the derivative to figure this out?

Re: Quick question about slope and finding f(x)

Quote:

Originally Posted by

**nappysnake** I know that but my qeustion was (maybe i didn't make it very clear..) when we know the VALUE of the SLOPE in a certain point X, does it translate to>> derivative f'(x) = value of slope, at that point?? Do i take the derivative to figure this out?

yes

you'd need the derivative expression to utilize the slope information