Question

Differentiation: The two tangents to the curve y=x^2 at the points where y=9 intersect at the point P. Find the coordinates of P.

Answer 1

this is what I think:
if y=9, then 9=x^2 implies x=3 and x=-3
the slope of the tangent line at x=3 and x=-3 can be found by finding the derivative.
If you write both equations of each line, you should get that they intersect the y-axis at the same point which is (0,-9)

Answer 2

wow, i was confused about what the question was asking for and now it makes complete sense.

Answer 3

thank you!

Answer 4

np

Answer 5

so i got the equations y=-6x-9 and y=6x-9. how do i solve for the intersecting point?

Answer 6

well look at the y-intercepts of each line

Answer 7

for future problems, how would i find the intercept if the linear equations didn't have the same y-intercept?

Answer 8

the y-intercepts are the same so they intersect at (0,-9)

Answer 9

set them equal to each other. my computer is going slow

Answer 10

before you crash, know i'm thankful haha

Answer 11

lol i can try to make a problem like this where the y intercepts are not the same

Answer 12

i get it it's ok :)

Answer 13

ok