differentiation help!!!?

Question

the normal to the curve y=x^2 +1 at the point where x=2, cuts the curve again at point P. Find coordinates P.

Answer is (-9/4 , 97/16)

thanks!

Answer 1

normal means perpendicular as the following :



y = x^2 + 1 ====> derivative

m = y ' = 2x ====> x = 2



m = 2 * 2

m = 4 <=====> since perpendicular, it will be as (-1/4)



when x = 2

y = 2^2 + 1 = 5 ====> (2,5)



y - y1 = m * (x - x1) =====> m = (-1/4) & (2 , 5)

y - 5 = (-1/4) * (x - 2)

y - 5 = (-1/4)x + (1/2)

y = (-1/4)x + (1/2) + 5

y = (-1/4)x + (11/2) <==== equation perpendicular



Now the perpendicular equation will cut the the original equation at P ( which is like saying somewhere ) meaning that we are going to find the intersection point as the following:



y = y

x^2 + 1 = (-1/4)x + (11/2)

x^2 + 1 + (1/4)x - (11/2) = 0

x^2 + (1/4)x - (9/2) = 0 =====> multiply the whole equation by 4

4x^2 + x - 18 = 0

(4x + 9)(x - 2) = 0



4x + 9 = 0 ====> x = -9/4

x - 2 = 0 ====> x = 2



when x = -9/4

y = (-9/4)^2 + 1

y = (81/16) + 1

y = (81/16) + 16/16

y = (97/16) <=====> P



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please e-mail me if u have a question

Answer 2

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Answer 3

i used to know this, but now im at uni and dont need to know it.

why did i asnwer this question, not knowing the answer you ask?

good question...