In mathematics, a linear approximation is an approximation of a general function using a linear function. They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.

Graphically,

Mathematically it is stated as:

y = f(a) + f’(a)(x-a)

where, f(a) = function curve

f’(a) = 1st derivative of curved function

x = x value of point (x,y) where the tangent line touches the curve f(a)

y = y value of point (x,y) where the tangent line touches the curve f(a)

For practicing the problems related to linear approximation in derivatives, you can try approximation calculator that provide you detailed solutions or related problems.