Make-up Reflection #2

Tangent Lines

Tangent lines can be used for many purposes. Finding a tangent line requires only a little knowledge of calculus but a substantial amount of algebra.

Example:

Find the line tangent to the graph y=2x²+4x+6 at x=1.

1. Identify the equation and point of tangency. If not given a y value, plug the x value into the original equation.

y=2x²+4x+6 y=2(1)<sup>2

2. Differentiate you equation.

dy/dx=4x+4


3. Plug in x value then solve for dy/dx.


dy/dx=4(1)+4=8




Your dy/dx value is your slope from here on you can create your equation of the tangent line. There are three forms that your equation can be presented in: point-slope, slope-intercept, or standard form. For these purposes, I am using point-slope.


(y-12)=8(x-1) is your final answer.


Another Example:

Find the line tangent to the graph y=x^3 that is parallel to the perpendicular graph of y=-(1/3)x.

1. Find the slope of the perpendicular line of y=-(1/3)x

-1/3 =m Perpendicular m=3

2. Set first derivative =3.

3x^2=3

3. Solve for x.

3x^2=3 x^2=1 x=1 x=-1

4. Plug x back into the original equation to find y values.

X^3 (1)^3 (-1)^3 y=1 y=-1

Final equations are y-1=3(x-1) and y+1=3(x+1)</sup>