Question

Find the linear approximation L (x) of the function F(x)=x^6+3x^2 at a=-1....L(x)=A+Bx where A=? and B=?

Answer 1

L = f(a) + f'(a)(x-a)...
L = x^6 + 3x^2 + (6x^5 + 6x)(x-a)...
L = (-1)^6 + 3(-1)^2 + (6(-1)^5 +6(-1))(x-(-1))...
L = 4 + (-12)(x+1)...
L = 4 -12x -12...
L = -8-12x...

Answer 2

so how do u figure out what a and b equal

Answer 3

Well wasn't it given:
L = A + Bx
quantish above solved:
L = -8 - 12x
L = A + Bx
A = -8; B = -12