Question

Find the area of the vegan bounded by the parabola y=x^2 the tangent line to this parabola at (1,1) and the x-axis.

Answer 1

area of the vegan? :) does your parabola eat no animal products?

Answer 2

oops i meant area of the region bounded by the parabola

Answer 3

Sorry Shyrene, idk. But since a parabola is a type of line, won't it be infinite, therefore haveng an infinite area?

Answer 4

idk? that's why im here asking for some help?.... if only they actually had examples like these in the book.

Answer 5

so we need to find the tangent line at (1,1) of y=x^2
do you know how to do that?

Answer 6

let me know what you get for the tangent line at (1,1) of y=x^2 ok?

Answer 7

and i will tell you if it is right or not. and did you see my drawing above?

Answer 8

tangent line y=2x?

Answer 9

you got y'=2 at x=1. so we have the slope of y=mx+b. so we have y=2x+b.
we need to find b the y-intercept. So we know a point (1,1) on the line.
so we have 1=2(1)+b. We solve this equation for b and get b=-1. so the tangent line to x^2 at (1,1) is y=2x-1

Answer 10

thank you i actually understood that.

Answer 11

np