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See attached file for full problem description.

1. Find dy for each of the following functions.
dx

a) y=3x^4-6x^2+2x

b) y=3/x^2

c) y=(8x^4-5x^2-2)/4x^3

d) y=square root 5x - square root x/5

2. a) Find the slope of the tangent to the curve y=4x^3-3x^2+1 at the point where x=-1.

b) Find the equation of the tangent to the curve y=2x-x2 that is perpendicular to the line x+4y-8=0.

3. If f(x)=320, find the derivative of f(x). Clearly give reason(s) for the answer.

4. Given f(x)=x3-1/2x^2+1. Find the value of x where dy =4.
dx

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The solution shows how to apply basic rules to calculate the derivatives of functions and equation of tangent line in detail.

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