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Derivative of a functions, slope of a curve

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Derivative of a functions, slope of a curve. See attached files for full problem description.

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(1), (2) and (3) there is no question about them in the scan

(4) Find slope at x=4 of f(x) = 7/x-sqrt(x)
----- f' = -7/x^2 -1/(2sqrt(x)) --- f'(4) = -7/16 -1/4= -11/16

(5) Find speed at t=3 s of s(t) = -16t^2+144t
---- the speed is s' = -32t + 144 = 48 feet per second

(6) f(x) = (4x-2)(6x-1) --- f' = 4(6x-1) +6(4x-2) = 48x -16

(7) y = x^3/(x-1) --- y' = [3x^2*(x-1) - 1*x^3]/(x-1)^2 = x^2(2x-3)/(x-1)^2

(8) y = (2x-1)(3x^2+1)/(2x+1) = (6x^3-3x^2+2x-1)/(2x+1) ---
--- y' = [(18x^2-6x+2)(2x+1) - 2(6x^3-3x^2+2x-1)] / (2x+1)^2 =
= ( 36x^3 -12x^2 +4x + 18x^2 -6x +2 -12x^3 +6x^2 -4x +2) / (2x+1)^2 =
= ( 24x^3 + ...

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