Question

find the line tangent to y= 10 sqrt x - x+3 at the points (100,3)

Answer 1

could you first get the derivative of y ?
because we need the slope to find the equation, and slope = dy/dx at that time.

Answer 2

wouldn't you use the y1-y2 = M( x1 - x2) equation?

Answer 3

ofcourse, but we need to find M = slope, right ?
\(\Large M= \dfrac{dy}{dx}|_{x=100}\)

Answer 4

so first find dy/dx :)
can u ?

Answer 5

i forget how to find the derivative of this one but i can try...

Answer 6

god :) if you get stuck, let me know, i'll help :)

Answer 7

**good

Answer 8

so i tried solving for y i plugged in 100 for x and got y=3 so would that be my y1?

Answer 9

do you know what derivative is ?

Answer 10

\(\Large \dfrac{d}{dx}x^n=n \times x^{n-1}\)
seen anything like this before ?

Answer 11

no not like that i'm sorry

Answer 12

(then how are you attempting a derivative Question, when it is not taught to you ?)


sqrt x = x^(1/2)
so put n =1/2 in that formula to get derivative of sqrt x first.

Answer 13

\[y = 10\sqrt{x} - x + 3 when (100,3) \]

Answer 14

so you want me to find the derivatives of the inside

Answer 15

soo would it be 5x^(-1/2) -1 ?

Answer 16

correct! :)
good.
now just put x= 100 there! and you will get the value of M

Answer 17

`slope of tangent to a curve at a point= derivative of the curve at that point`

Answer 18

so M = 22.360679775?

Answer 19

jow :O which calculator did u use ?
\(\large M = 5 \times 100^{-1/2}-1 = 5 \times \dfrac{1}{\sqrt{100}}-1=5/10 -1=-1/2 \)
got this ?

Answer 20

oh jeez yes you're rihgt

Answer 21

so we have M =-1/2
x1 =100, y1 =3
just plug these in
y1-y2 = M( x1 - x2)
and you'll get the equation of line :)

Answer 22

3 - y^2 = 1/2(100 -x^2) don't i need another variable?

Answer 23

how did u get y^1 and x^2 ?