# Thread: equation of the tangent line

1. ## equation of the tangent line

Find the equation of the tangent line to the following curve at the given point P. Illustrate by graphing the curve and the tangent line on the same screen.

1

Here are the steps:
I did it according to this Find the equation of the tangent line to the following curve at the given point P. ? - Yahoo! Answers

y=6-2x^(1/2)
6-2(1)^(1/2)
y=4

y-4=4(x-1)
y-4=4x-4

y=4x (and it's WRONG T_T)

2. Originally Posted by greenbee
Find the equation of the tangent line to the following curve at the given point P. Illustrate by graphing the curve and the tangent line on the same screen.

1

Here are the steps:
I did it according to this Find the equation of the tangent line to the following curve at the given point P. ? - Yahoo! Answers

y=6-2x^(1/2)
6-2(1)^(1/2)
y=4

y-4=4(x-1)
y-4=4x-4

y=4x (and it's WRONG T_T)

$y = 6x - 2\sqrt{x}$

$y' = 6 - \frac{1}{\sqrt{x}}$

3. Originally Posted by skeeter

$y = 6x - 2\sqrt{x}$

$y' = 6 - \frac{1}{\sqrt{x}}$
how do i make the equation including the points?

4. Originally Posted by greenbee
how do i make the equation including the points?
use the point-slope form of a linear equation ...

$y - y_1 = m(x - x_1)$

where $(x_1,y_1)$ is your point, and the slope is $m = f'(x_1)$

5. Originally Posted by skeeter
use the point-slope form of a linear equation ...

$y - y_1 = m(x - x_1)$

where $(x_1,y_1)$ is your point, and the slope is $m = f'(x_1)$
thank you!!!