Problem

15 Point $A$ lies on the curve $y=x^{2}+5 x+8$ The $x$-coordinate of $A$ is -4 15 (a) Show that the equation of the normal to the curve at $A$ is $3 y=x+16$

Solution

Step 1 :Find the coordinates of point A: (-4, 4)

Step 2 :Find the derivative of the curve equation: y' = 2x + 5

Step 3 :Find the slope of the tangent at point A: -3

Step 4 :Find the slope of the normal: 1/3

Step 5 :Use the point-slope form to find the equation of the normal: y - 4 = 1/3(x + 4)

Step 6 :Simplify the equation: 3y = x + 16

Step 7 :Check the equation meets the requirements

Step 8 :Box the final answer: \boxed{3y = x + 16}

From Solvely APP
Source: https://solvelyapp.com/problems/8373/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download