Linear Approx?

Question

Let f(x) = (x^2) - 5x and find the linear approximation L(x) to f at x=6. Solve the equation L(x)=0

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 a 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