MATH 1306 – Homework Handout # 7

Answers To Odd-numbered Problems

1a.       i)  [slope of tangent line at input 0] = f '(0) = -6

            ii)  coordinates of possible turning points are (x, y) = (3, -16)

                Justification:

                To find x: solve f '(x) = 0 or 2x-6 = 0. You get x=3.

                To find y: y = f'(3) = (3)² - 6(3) - 7 = -16

1b.       i)  [slope of tangent line at input 0] = g '(0) = -3

            ii)  coordinates of possible turning points are (1/3, -14/27) ≈ (0.3, -0.5)

3a.       g '(1) = -12 and so the function g is decreasing at the input x = 1

3b.       g '(3) = 24 and so the function g is increasing at the input x = 3

3c.       The turning point (2, -20) is a valley on the graph of g since the function changes from decreasing to increasing at x=2.

5.       i)  y-intercept = f(0) = 2

          ii) x-intercepts are x = -1, x = 1, x = 2

          iii) coordinates of the possible turning points are approximately (-0.2, 2.1) and (1.5, -0.6)

               Hint: Use the quadratic formula x = [ -b + √(b² - 4ac) ]/2a

         iv) coordinates of the possible inflection point are approximately (2/3, 0.7) ≈ (0.7, 0.7)

         v) a possible graphing window is [ -2, 3] x [-1, 3]

             Note: Different persons may answer differently.

7a.       i)  y-intercept = f(0) = -21

           ii) x-intercepts are x = -3, x = 7

           iii) [slope of tangent line at input 0] = f '(0) = -4

           iv) coordinates of possible turning points are (2, -25)

           v) a possible graphing window is [ -4, 8] x [-17, 17]

7b.       i)  [slope of tangent line at input 0] = g '(0) = -12

           ii) coordinates of possible turning points are (-2, 16) and (2, -16)

           iii) a possible graphing window is [ -4, 4] x [ -17, 17]