Question

Find an equation of the tangent line to the curve at the given point.
y =square root of x (9,3)

Answer 1

First, you get the derivative of x^.5.
Then, you plug in x=9 into the derivative to get you the instantaneous rate of change at x=9.
Then, plug that slope, along with the point (9,3), into y=mx+b and solve for b.
Then, still use the instantaneous slope that you found, and plug that in, along with the b you found, into y=mx+b
Lastly, be happy you (hopefully) got the right answer.
Any questions?

Answer 2

why x^5? @JonnyVonny

Answer 3

x^.5

Answer 4

That is the square root of x.

Answer 5

so the derivitive is 1/2x

Answer 6

@JonnyVonny

Answer 7

No, sorry, 1 sec.

Answer 8

Okay, so, you have to do the chain rule to take the derivative of (x)^.5

Answer 9

is it 1/2x @JonnyVonny

Answer 10

No, it is .5x^-.5\[\frac{ 1 }{ 2 \sqrt{x} }\]

Answer 11

Do you see how?

Answer 12

i got y=1/6x+3/2