Question

Find the linear approximation L(x) of the function f(x)=x^7+3x^3 at a=−1

L(x)=A+Bx where A= ??? B=???

Answer 1

It's just the tangent line.

Answer 2

\[
L(x) = f'(x_1)(x-x_1)+f(x_1)
\]

Answer 3

In this case \(x_1=a\)

Answer 4

L(x)=f′(-1)(x−(-1))+f(-1) ?

Answer 5

Don't overthink it and memorize a formula. f'(a) gives you the slope of the line at that point (a, f(a)). You also have the point. So you can write the point-slope formula of the line
y-y0=m(x-x0)