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MATH 1100: QUANTITATIVE ANALYSIS TEST #2 (VERSION A) Name: This test has 4 pages and 4 problems. No calculators are allowed. You are permitted only a pencil or pen. Work out everything as far as you can before making decimal approximations. 1. Find the derivative with respect to x of 1/3 y = x2 + 1 . Date: September 24, 2001. 1 2 MATH 1100: QUANTITATIVE ANALYSIS 2. Find the tangent line to the curve y = x5 − x3 at x = 1. TEST #2 (VERSION A) MATH 1100: QUANTITATIVE ANALYSIS TEST #2 (VERSION A) 3 3. The response y of the body to an amount x of adrenalin is given by x y= a + bx where a and b are constants determined by experiment. (a) Where is this function continuous? (b) Suppose that for any x ≥ 0 the value of y can not be negative. What can you say about a and b? Explain your answer. (For example, are they both positive, both negative, or of opposite signs?) 4 MATH 1100: QUANTITATIVE ANALYSIS TEST #2 (VERSION A) 4. A product has sales S (in millions of dollars) given as a function of time t (in months) by 1 S =1+ . (t + 1)5 (a) Find the rate of change of sales at time t = 1. (b) Find the second derivative of sales at t = 1, and use it to explain how the rate of sales is changing at t = 1.