121616949-math.116 - 102 Chapter 5 Curve Sketching 15 y =(x...

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102 Chapter 5 Curve Sketching 15. y = ( x + 5) 1 / 4 16. y = tan 2 x 17. y = cos 2 x - sin 2 x 18. y = sin 3 x 19. Identify the intervals on which the graph of the function f ( x ) = x 4 - 4 x 3 + 10 is of one of these four shapes: concave up and increasing; concave up and decreasing; concave down and increasing; concave down and decreasing. 20. Describe the concavity of y = x 3 + bx 2 + cx + d . You will need to consider different cases, depending on the values of the coefficients. 21. Let n be an integer greater than or equal to two, and suppose f is a polynomial of degree n . How many inflection points can f have? Hint: Use the second derivative test and the fundamental theorem of algebra. A vertical asymptote is a place where the function becomes infinite, typically because the formula for the function has a denominator that becomes zero. For example, the reciprocal function f ( x ) = 1 /x has a vertical asymptote at x = 0, and the function tan x has a vertical asymptote at x = π/ 2 (and also at x = - π/ 2, x = 3 π/ 2, etc.). Whenever the formula for a
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