Derivatives Help Please

[Guest TheGuyWhoKnowz]

I have some Calculus assignments and I almost finish them, however there are 3 left and I have no idea How to do them, Can you please please help me, I need at least a C or B for this class.

 

*Find the Derivative

 

h(x) = x/(1-x)³ . Also find the coordinates of any point on the graph of the given function for which tangent line is horizontal. (I don’t know what this is)

 

*Find derivative

 

Y = cos(x-1) / (x-1)

 

*Find a function form f(x) = a + bcoscx that is tangent to the line y = 1 at the point (0,1) and tangent to the line

 

y = x + 3/2 – Ð/4 at the point (Ð/4 ,3/2)

[fafalone]

y=x/(1-x)^3

 

...quotient rule

(uv' - vu')/v^2, u=x, v=(1-x)^3

 

x(3(1-x)^2*(0-1)) - (1-x)^3

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((1-x)^3)^2

 

i hate algebraic simplification, so you can go from there

an alternative is to use implicit differentiation... but i doubt that's what your teacher is looking for here.

 

A horizontal line has a slope of zero... so just find where y' is zero.

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y=cos(x-1)/(x-1)

...this is just the quotient rule again, d/dx uv = (uv' - vu')/v^2

 

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i'll look at the 3rd one later...

 

don't just copy down my solutions, because i don't have my ti-89 handy i can't check things, so odds are i amde a mistake somewhere