$4 Consider the quartic polynomial f(:c) = ? 1.51::3 + 13.5w2. f(a:) has two inflection points at a: = C and a: = D with C S D For each of the following intervals, determine whether f(:c) is concave up or concave down. ( 00, C): Select an answer , a (C, D): Select an answer a (D, 00): Select an answer The graph of f(:c) shown below will help you determine whether your answers are reasonable, but you need to use Calculus to determine the exact answers. mm$$$1$$ -5-4-3-2-I 123Q Check Answer ' Second Derivative Test 1. Find the first derivative of the function g(:z;) = 6:1:3 + 18$2 1441;. m, = :1 2. Find the second derivative of the function. W) = :] 3. Evaluate g"( 4). g"( - 4) = :J 4. Is the graph of 9(2) concave up or concave down at a: = 4? At a: = 4 the graph of 9(3) is concave :] 5. Does the graph of g(a:) have a local minimum or local maximum at a: = 4? At a: = 4 there is a local [: \\ CheckAnswer \\