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)
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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].
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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
