
Mean Value Theorem
I am having a problem with coming out with the right answer for the following problems, please help.
Using the Mean Value Theorem. If f(x)=sin(x) on the interval [1, 1.15] what is c.
okay the Mean Value Thoerem is f'(c) = f(b)f(a)/ba
so I have 1.151/.15, so tell me if I'm on the right track,if not please help.
Next problem
Sin(x)+ln y and 0<x<pi/2, using implicit differntiation, what is dy/dx.
Where do I start?
Thanks

On the first one, you are on the right track, but one thing. You found the ycoordinate of c, which is f(c). They want to know the xcoordinate, c. So, set sin(x)=f(c) (the value you got) and solve for c.
$\displaystyle sin(c)=\frac{sin(1.15)sin(1)}{1.151}$
On the second one, you know that sin(x)+ln(y) must equal some constant correct? So set it up like this.
$\displaystyle sin(x)+ln(y)=c$
$\displaystyle cos(x)+\frac{1}{y}*\frac{dy}{dx}=0$
See how that works? I'm sure you can finish it from there. :)