Thread: equation for the line tangent to graph

1. equation for the line tangent to graph

hey i have im practising some problems and i dont know where to start on this question.

find an equation for the line tangent to the graph of y = secx at (pie/3,2)

any suggestions?

2. 1) Verify that (pi/3,2) is ON the graph. This is a point on the line.

2) Find the derivative of the function, y' = ???

3) Evaluate the derivaive at x = pi/3. This is the slope of the line.

4) Remember your algebra and use the Point-Slope form of a line.

3. Originally Posted by TKHunny
1) Verify that (pi/3,2) is ON the graph. This is a point on the line.

2) Find the derivative of the function, y' = ???

3) Evaluate the derivaive at x = pi/3. This is the slope of the line.

4) Remember your algebra and use the Point-Slope form of a line.
thank u ! ill give it a go and post it

4. $
y = secx
$

$
y' = tanx \cdot secx
$

input x = $\frac{\pi}{3}$ into:

$
y' = tan(\frac{\pi}{3}) \cdot sec(\frac{\pi}{3})
$

$
m = 2 \cdot \sqrt{3}
$

now y - y1 = m(x - x1) formula to get the equation

$

y - 2 = 2 \cdot \sqrt{3}(x - \frac{\pi}{3})

$

is that the correct path?

5. Yes.

6. Originally Posted by jvignacio
$
y = secx
$

$
y' = tanx \cdot secx
$

input x = $\frac{\pi}{3}$ into:

$
y' = tan(\frac{\pi}{3}) \cdot sec(\frac{\pi}{3})
$

$
m = 2 \cdot \sqrt{3}
$

now y - y1 = m(x - x1) formula to get the equation

$

y - 2 = 2 \cdot \sqrt{3}(x - \frac{\pi}{3})

$

is that the correct path?
Did you do my Step #1? You can be assured I would put one on the exam that was NOT actually on the curve.

Other than that...AWESOME!!

7. Originally Posted by TKHunny
Did you do my Step #1? You can be assured I would put one on the exam that was NOT actually on the curve.

Other than that...AWESOME!!

thakns mann!!
how do i check if its on the graph?

8. Plug in the x coordinate given into the function and see if it matches with the y coordinate given.

9. Originally Posted by 11rdc11
Plug in the x coordinate given into the function and see if it matches with the y coordinate given.
yes it does! both 2

10. NOW we're done.

When the sneaky one shows up, you'll be the only one to get it right.