w05e - is known about them: f (2) =-3 f (2) = 5 g (2) = 1 g...

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Math 151, Workshop 5 1. Let f ( x ) = 5 x 2 - 10 x e x . a) Graph y = f ( x ) in the window 0 x 5 and - 3 y 1. Locate the apparent highest and lowest points on the curve. b) Calculate f ( x ) and use it to locate (algebraically) all those values of x at which the graph has a horizontal tangent line. Check your answer against a). c) Use f ( x ) to Fnd an equation for the line that is tangent to the curve y = f ( x ) at x = 1. Draw the line on the graph in a) to check the result. d) Use the graph in a) to guess the values of x where f ( x ) is largest and where f ( x ) is smallest. Then graph the equation y = f ( x ) on your calculator to check your guesses. y x (-1,1) (1,1) 2. A circle with center on the y -axis is tangent to the parabola y = x 2 at the points (1 , 1) and ( - 1 , 1). ±ind its center and radius. A diagram is shown to the right. Suggestion: ±ind the equation of the normal line to y = x 2 at the point (1 , 1), that is, the line that is perpendicular to the parabola (and circle) at (1 , 1). How can this be used to Fnd the circle’s center? 3. Suppose that f ( x ) and g ( x ) are di²erentiable functions, and the following information
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Unformatted text preview: is known about them: f (2) =-3 f (2) = 5 g (2) = 1 g (2) = 2 g (0) = 2 g (0) = 4 a) If F ( x ) = f ( x ) g ( x ) , compute F (2) and F (2). b) If G ( x ) = x 3 f ( x )-7 g ( x ), compute G (2) and G (2). c) If H ( x ) = 3 + e x g ( x ) , compute H (0) and H (0). 4. our containers are each 10 cm tall (see Fgure). Each of them has a volume of 30 cm 3 and each is being Flled by a liquid at the rate of 5 cm 3 per minute. Here is a picture of the containers: a) or each of the containers, graph the height, h ( t ), of the level of the liquid in the containers measured in centimeters as a function of time, t , measured in minutes. b) Which of the functions graphed in a) are continuous? Explain your answers. c) Which of the functions graphed in a) are dierentiable? Explain your answers. 10 cm (A) (B) (C) (D)...
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This note was uploaded on 03/24/2011 for the course PHYSICS 123 taught by Professor Madey during the Spring '08 term at Rutgers.

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w05e - is known about them: f (2) =-3 f (2) = 5 g (2) = 1 g...

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