finding unknown constants in a function using calculus...

hello, so i'm stuck on this problem where im given the function with constants and the point it passes through and the second derivative and first derivative at that point but i cant figure out how to find the constants.... please help...

so here is the question,

*The curve of y= x^4 + ax^2 + bx + c, passes through the point ( -1 , -8) and at that point f ''(x) = f '(x) = 6. find the values of a, b, and c and sketch the curve. *

i dont get what *f ''(x) = f '(x) = 6 *actually means so please clear it up for me as well as how to find the values of a,b,and c.

thanks in advance

Re: finding unknown constants in a function using calculus...

Quote:

Originally Posted by

**bakerkhojah** hello, so i'm stuck on this problem where im given the function with constants and the point it passes through and the second derivative and first derivative at that point but i cant figure out how to find the constants.... please help...

so here is the question,

*The curve of y= x^4 + ax^2 + bx + c, passes through the point ( -1 , -8) and at that point f ''(x) = f '(x) = 6. find the values of a, b, and c and sketch the curve. *

i dont get what *f ''(x) = f '(x) = 6 *actually means so please clear it up for me as well as how to find the values of a,b,and c.

thanks in advance

Given $\displaystyle f(x)= x^4 + ax^2 + bx + c$. Your have three unknowns $\displaystyle a,b,c$

You have three equations

$\displaystyle f(-1)= -8$

$\displaystyle f'(-1)= 6$ (first derivative)

$\displaystyle f''(-1)= 6$ (second derivative)

Can you solve for $\displaystyle a,b,c$?

Re: finding unknown constants in a function using calculus...

Assuming that f'(-1)=f''(-1)=6 we obtain:

a = -3

b = 4

c = 14