QUIZ #3: CALCULUS 1A (Stankova) Wednesday, February 11, 2004 Section 10:00–11:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1.

(a) Find the slope of the tangent to the parabola y = 1 − 3x + x^{2} at the point where x = a.

(b) Find the slope of the tangent lines at the points whose x-coordinates are (i) 0 and (ii)1.

QUIZ #3: CALCULUS 1A (Stankova) Wednesday, February 11, 2004 Section 11:00–12:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. Prove that the equation

x^{4} − 3x^{2} = 13

has at least one real root. Please verify in writing all hypotheses and conditions of any theorem you apply and explain your work.