TANGENT LINE/ NORMAL LINE Aimen Abbasi and Jael Navarro

Tangent Line (x, y)

5 steps 1. Plug in x to your original equation 2. Derive 3. Plug in x to your derived equation 4. Plug in to point intercept form 5. Chang it to y – intercept form

STEP 1 y = x^3 - 2x + 5 at x=2 y = (2)^3 - 2(2) + 5 y = 9 - You are given: y = x^3 - 2x + 5 at x=2 - To find y, you need plug in x to your original equation y = (2)^3 - 2(2) + 5 y = 9

STEP 2 - Derive y = 3x^2 - 2

STEP 3 - Plug in your x to your derived equation y = 3(2)^2 - 2 = 10 SLOPE!

STEP 4 y –y1 = m(x + x1) y –9 = 10(x + 2) - Plug it in to Point Intercept Form y –y1 = m(x + x1) y –9 = 10(x + 2)

STEP 5 Change it into y intercept form y= 10x - 11

Lets try another - You are given X^2 + 2x – 3 at (1, 0 )

Next Step 2 is - Differentiate 2X + 2 - Plug it in 2(1) + 2 = 4 SLOPE!

Point – Slope Form y – 0 = 4 (x - 1) y = 4 x - 4 - Plug it in - Change to standard y = mx +b y = 4 x - 4

Graph your line y = 4 x - 4

Lets Practice ! - Find the tangent lines of the following