Let f(x) = 1/x^2 (a) use the definition of the derivatve to find f'(x). (b) find the equation of the tangent line at x=2

(a)

(b)

Step-by-step explanation:

The given function is

                 .... (1)

According to the first principle of the derivative,

Cancel out common factors.

By applying limit, we get

                        .... (2)

Therefore .

(b)

Put x=2, to find the y-coordinate of point of tangency.

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

Substitute x=2 in equation 2.

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.