MATH 221 – Calculus I – Test 1 Name________________

Instructions: Answer all the questions on the test paper provided and show all your work so that partial credit may be given. You may use a calculator for any problem on this test.

1. Let f(x) = 1 – 2x - 4x² . Find using the limit definition of the derivative. Show all your steps. (20)

2. Solve the inequality and express your solution in interval notation. (20)

3. Find and classify the discontinuities of the following function. Show all the necessary limits and carefully indicate your answers. (15)

4. Let . (20)

a) Find the equation of the line tangent to the graph of f(x) at the point given by x = -2.

b) Find all points on the graph of y = f(x) at which the tangent lines are parallel to the line given by y = 15x + 2.

c) Find all points on the graph of y = f(x) at which the tangent lines are perpendicular to the line given by .

6. Sketch the graph of a function, f(x), such that f(3) = 3, f(-1) = -2, f has an infinite discontinuity at x = 1, f has a removable discontinuity at x = -1, f has a jump discontinuity at x = 3, and (15)

6. Sketch the graph of a function which is continuous at x = 0 but is not differentiable at x = 0. (5)

7. Let f(x) be defined by: (5)

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Find