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Unformatted text preview: MATH 125 Spring 2008 – Quiz 3 Name 1. (6 points) Diﬀerentiate the following functions with respect to x: (a) f (x) = cos(x2 ) (b) h(x) = (x3 + 1) cos(x2 ). Hint: One may compute (b) using the result of (a). 2. (6 points) Let f (x) = 2x . x+1 a) Write f (x) in terms of x. b) Find x-intercept of tangent line to the curve y = f (x) at point (1, 1). 1 3. (8 points) A particle is moving along a straight line with position (measured in feet) given by s(t) = −t3 + 6t2 − 9t + 2, where t is measured in seconds. Write proper units for your answers. (a) Find the velocity at time t. (b) Determine when the velocity is zero. (c) When is it moving backward? (d) Find the total distance traveled by the particle during the ﬁrst six seconds. 2 Brief Answer: 1. a) (cos x2 ) = cos (x2 ) · (x2 ) = −2x sin x2 . b) h (x) = (x + 1) cos x2 + (x + 1)(cos x2 ) = cos x2 − 2x2 sin x2 − 2x sin x2 . 2. a) y = b) y is −1. 3. a) v (t) = −3t2 + 12t − 9 (f/s). b) t = 1, 3 second c) Solve v (t) < 0, then when 0 < t < 1 and t > 3 seconds, it’s moving backward. d) Total distance is |s(1) − s(0)| + |s(3) − s(1)| + |s(6) − s(3)| = 62 feet.
2 (x+1)2 |x=1 = 1 . 2 by quotient rule So the equation of tangent line is y = 1 x + 1 . Hence, x-intercept 2 2 3 ...
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