# Math Help - Derivative help Calc 1

1. ## Derivative help Calc 1

I have a homework assignment due tonight, and I feel like this guy ---->

Here are the two questions I still do not understand

1.) Write in slope intercept form the equation for the tangent line for the curve y=sin(x) at x=(pi/3).

What I do know is the f'(x)=cos(x).
Next, do I plug pi/3 into the derivative?? I'm lost at this point.

2.) Use the definition of the derivative to compute the derivative of f(x) = squareroot(x-3)

so.. f(x)=(x-3)^(1/2)
could I do f(x)=(1/2)(x-3)^(-1/2) ?
and where would I go after that?

2. Originally Posted by bassman111
I have a homework assignment due tonight, and I feel like this guy ---->

Here are the two questions I still do not understand

1.) Write in slope intercept form the equation for the tangent line for the curve y=sin(x) at x=(pi/3).

What I do know is the f'(x)=cos(x).
Next, do I plug pi/3 into the derivative?? I'm lost at this point.

the slope at x = pi/3 is f'(pi/3)

2.) Use the definition of the derivative to compute the derivative of f(x) = squareroot(x-3)

$\textcolor{red}{f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}}$

$\textcolor{red}{f(x) = \sqrt{x-3}}$

$\textcolor{red}{f(x+h) = \sqrt{x+h-3}}$
...

As a quick follow up, if f(x)=cos(3x) does f'(x)=-3sin(3x)?

4. Originally Posted by bassman111

As a quick follow up, if f(x)=cos(3x) does f'(x)=-3sin(3x)?
that would be correct.

5. Thank you for the help

6. ok so if the derivative of the function is cos(x) and you plug in pi/3 in for x, and you check the unit circle you see that it is 1/2. So the slope then would be 1/2.

Then when you put in pi/3 in the original equation you can get the (sqrt3)/2 as the y coordinate. Then y1-y2 = slope(x1-x2).

y - (sqrt3)/2 = 1/2(x-pi/3)

y= 1/2(x)- (pi/6) + (3(sqrt3)/6)

then you have a standard y= mx+b by just doing the calculations. The only way to clean it up is to plug keep the decimal answer. So it would be:

1/2x + 0.34342663

But my answers aren't matching up with the previous advice, so maybe I'm missing something. I also need to apologize for not writing in cool math pictures. Hope this works, it will take me time to learn how to do that.

7. As for your other problem with the definition of derivative, I'm getting

$\frac{1}{2\sqrt(x-3)}$