Linear approximation help please?

Question

Can somebody explain how to do this?

http://images31.fotki.com/v1041/photos/7/70549/1058975/lapproximation-vi.jpg


I'd appreciate any help. Thanks.

Answer 1

The linear approximation at a point P is just the tangent line through that point.

The slope of the tangent line is the derivative of the function at P.

If a line has slope M and goes through point then it has the equation:

(y-Y)/(x-X) = M or y = M(x-X) + Y