Find the local linear approximation L(x) of the function f(x)=x^2+3 at x=1 .

Question

It will be really helpful if you describe briefly.

Answer 1

Here you'll want to form the equation of the tangent line at the point x = 1. The slope of this line will be the value of the derivative at 1. Then use the point slope form of a line, and you have your linear approximation. Another way to think of this equation is as a Taylor series approximation to the curve centered at 1 which is only taken out to first order, in other words just two terms.