1. What is the derivative of h(x) = 42?

2. Find the derivative of y = 4x³ - 2x + 7

3. If f(x) = x⁴, determine the value of x where the slope of a tangent is 108.

4. What is the velocity of a particular object at time t = 2 if the displacement is s(t)=2t²+5?

5. What is the equation of the tangent to the curve y=2x³-3x² at the point (2,4)?

6. A ball's height, h, in metres above the ground after t seconds, is given by h(t)=-5t²+30t, t0. Determine the value for t when the ball is at its maximum height.

7. A population of a bacteria colony after t hours is given by n=50+30t-20t². Determine the growth rate after 2 hours.

8. The cost of producing x units of a product is given by C(x)=-0.003x²+4x+3000. The revenue function is given by R(x)=130x-0.203x². Determine the marginal profit when the 100th unit is produced. Attach a complete solution using good form. [Watch the negatives! In the cost equation the 0.003 is negative]

9. Differentiate y=(3x+1)⁸(2x-5)⁷. Show all steps. Express your final answer in factored form. Attach a complete solution using good form.