Pre-Calc Homework Solutions 132

Pre-Calc Homework Solutions 132 - 132 Section 4.2 44....

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44. continued Note that 2} 1 2 } x 2 } 1 2 } 5 0 when x 52 1, and 3 x 2 2 12 x 1 8 5 0 when x 5 5 } 12 6 6 ˇ 4 w 8 w }5 2 6 } 2 ˇ 3 3 w } . But 2 2 } 2 ˇ 3 3 w } < 0.845 , 1, so the only critical points occur at x 52 1 and x 5 2 1 } 2 ˇ 3 3 w } < 3.155. 45. Graph (c), since this is the only graph that has positive slope at c . 46. Graph (b), since this is the only graph that represents a differentiable function at a and b and has negative slope at c . 47. Graph (d), since this is the only graph representing a function that is differentiable at b but not at a . 48. Graph (a), since this is the only graph that represents a function that is not differentiable at a or b . 49. (a) V ( x ) 5 160 x 2 52 x 2 1 4 x 3 V 9 ( x ) 5 160 2 104 x 1 12 x 2 5 4( x 2 2)(3 x 2 20) The only critical point in the interval (0, 5) is at x 5 2. The maximum value of V ( x ) is 144 at x 5 2. (b) The largest possible volume of the box is 144 cubic units, and it occurs when x 5 2. 50. (a)
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