question archive Find the equations of all tangent lines to the graph of y = x" + 2 x + 36 that pass through the origin (0, 0)

Find the equations of all tangent lines to the graph of y = x" + 2 x + 36 that pass through the origin (0, 0)

Subject:MathPrice:9.82 Bought3

Find the equations of all tangent lines to the graph of y = x" + 2 x + 36 that pass through the origin (0, 0). Fill in the blanks in parts (a) and (b). (@) How many tangent lines to the graph of y = x" + 2 x + 36 pass through the origin (0, 0)? (Please input a number, not the word for the number.) The number of tangent lines that pass through (0, 0) is . (b) List the slope-intercept form for the equation(s) of the tangent line(s) to the graph of y = x" + 2 x+ 36 that pass through (0, 0). Please put a comma between multiple equations, if needed. If there are no tangent lines that pass through (0, 0), then enter NONE. The equation(s) of the tangent lines that pass through (0, 0) is/are].

pur-new-sol

Purchase A New Answer

Custom new solution created by our subject matter experts

GET A QUOTE

Answer Preview

2 tangent lines

y=-10x,y=14x

 

Step-by-step explanation

1. Given: y=x2+2x+36   (1)

Solve for y'

y'=2x+2  at (0,0)

(y-0)=(2x+2)(x-0)

y=2x2+2x     (2)

Because the line must touch the curve, we may substitute y=x2+2x+36   (1)

equate (1) and (2)

x2+2x+36=2x2+2x  Cancel out 2x

x2-36=0

(x-6)(x+6)

x=6,-6

 

There are 2 tangent line

m=2x+2

m=2(6)+2

m=14

at x=-6

m=2(-6)+2

m=-10

 

y=-10x

y=14x