Question

find the slope and equation of the tangent line to the graph of f at point P(4, 14)

f(x) =x^2 -2

Step 1

Given a function f(x) shown below. Here we need to determine slope and the equation of tangent line passing through (4,14).

Step 2

The tangent of a curve at point P is representation of rate of change of curve at that particular point. So The slope of a tangent line at point P of a curve is nothing but the derivative of the function at that point P.

So for a given function f(x) and point P on it. The slope of tangent line at point P os given by f'(x) at point P.

Step 3

We know f(x) and now we compute f'(x) we get the following. We know that we need the slope of the tangent line at point (4,14) So we substitute x ...

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