For problems 1 - 12 find the derivative of the given function.

1. f(x)=6x39x+4f(x)=6x39x+4
2. y=2t410t2+13ty=2t410t2+13t
3. g(z)=4z73z7+9zg(z)=4z73z7+9z
4. h(y)=y49y3+8y2+12h(y)=y49y3+8y2+12
5. y=x+83x24xy=x+8x32x4
6. f(x)=105x3x7+63x83f(x)=10x35x7+6x833
7. f(t)=4t16t3+8t5f(t)=4t16t3+8t5
8. R(z)=6z3+18z413z10R(z)=6z3+18z413z10
9. z=x(3x29)z=x(3x29)
10. g(y)=(y4)(2y+y2)g(y)=(y4)(2y+y2)
11. h(x)=4x37x+8xh(x)=4x37x+8x
12. f(y)=y55y3+2yy3f(y)=y55y3+2yy3
13. Determine where, if anywhere, the function f(x)=x3+9x248x+2f(x)=x3+9x248x+2 is not changing.
14. Determine where, if anywhere, the function y=2z4z33z2y=2z4z33z2 is not changing.
15. Find the tangent line to g(x)=16x4xg(x)=16x4x at x=4x=4.
16. Find the tangent line to f(x)=7x4+8x6+2xf(x)=7x4+8x6+2x at x=1x=1.
17. The position of an object at any time t is given by s(t)=3t440t3+126t29s(t)=3t440t3+126t29.
    1. Determine the velocity of the object at any time t.
    2. Does the object ever stop changing?
    3. When is the object moving to the right and when is the object moving to the left?
18. Determine where the function h(z)=6+40z35z44z5h(z)=6+40z35z44z5 is increasing and decreasing.
19. Determine where the function R(x)=(x+1)(x2)2R(x)=(x+1)(x2)2 is increasing and decreasing.
20. Determine where, if anywhere, the tangent line to f(x)=x35x2+xf(x)=x35x2+x is parallel to the line y=4x+23y=4x+23.