Question

# 1) let f(x) = 2x + px + q. Find the values of p and q such that f(1) = 3 is an extreme value of f on [0,2]

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2) If p(x) is a polynomial such that p'(x) has a simple root at x = 1 , then has a relative extrema at x = 1 (true/ false)

3) If a function f is continuous on [a, b] , then f has an absolute maximum on [a, b]. (true/false)

4) Find all values of C that satisfy the conclusion of Rolle’s Theorem for the function f(x) = x2 – x on the interval [0, 1].

5) If f(x) = 0 has a root, then Newton’s Method starting at x = x1 will approximate the root nearest x = x1 . (true /false)

6) Newton’s Method uses the tangent line to y = f(x) at x = xn to compute xn + 1. (true / false)

7) Rolle’s Theorem says that if f is a continuous function on [a, b] and f(a) = f(b) , then there is a point between a and b at which the curve y = f(x) has a

horizontal tangent line. (true / false)

8) Use Newton’s Method to approximate cos x = x

9) If a function f has an absolute minimum on (a, b), then there is a critical point of f at (a, b). (true/false)

10) If a function f is continuous on [a, b] and f has no relative extreme values in (a, b), then the absolute maximum value of f exists and occurs either at x = a or at x = b. (true/false)

Math