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.

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.