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FA21 MATH 154 Midterm Exam

1. Determine the domain of 

2. Evaluate the following limit:

3. Compute the derivative of 

4. A company’s cost function is Use marginal cost to estimate the cost of producing the item.

5. Determine when the function  is increasing.

6. Determine the value of a for which the function is continuous everywhere:

7. An investment of $20,000 grows at a rate of 4% compounded continuously. How much interest is earned during the second year?

8. Find the slope of the tangent line to the curve defined by  at the point (1, 1).

9. Suppose  Find the equation of the line tangent to y = h(x) at x = 4.

10. Suppose that f(x) is a differentiable function such that  Determine the value of f0 (2).

11. Consider the demand equation  for some commodity where 0 ≤ p ≤ 6 denotes the price per unit and q denotes the quantity of units demanded. Determine the price for which the demand is unitary (i.e. E(p)=1).

12. Find and identify all the local extrema (local max and min) of the function 

13. Use the Intermediate Value Theorem to prove the function  has a critical number.

14. Determine the point on the curve y = ln x whose tangent line goes through the point (0, 1).