Derivative problem fxx22x to find the equation of the secant

Derivative problem, f(x)=x^2+2x, to find the equation of the secant line.
Find the equation of the secant line through the points where x has the given values, x=3 and x=5

Solution

A secant line is a line that passes through 2 point on the curve. Our curve being f(x) = x2 + 2x.

Hopefully you know how to find the equation of a line given 2 points. i.e. find the slope and y-intercept.

Let\'s get the 2 points. plug in 3 and 5 into the function separately.

32 +2(3) which is 15, thus giving us the point (3,15)

and 52 +2(5) which is 35, thus giving us the point (5,35)


Now find the slope using the fraction: (y1- y2) / (x1 - x2) ---> (15 - 35) / (3 - 5) = -20 / -2 = 10

Use slope intercept form: y = mx + b and plug in you slope as m, and either (3, 15) or (5, 35), doesn\'t matter which.

Solve for b and that is your y intercept. then rewrite as y =__x + ___ putting in your slope and y-intercept that you just found.