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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 find 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). Find its center and radius. A diagram is shown to the right. Suggestion: Find 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 find the circle’s center? 3. Suppose that f ( x ) and g ( x
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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 di²erentiable? Explain your answers. 10 cm (A) (B) (C) (D)...
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