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# classwork6 - point, but what does this tell us about our...

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Classwork VI Sections 3.7, 3.8 Find the equation of the line tangent to y = x 3 + 3 x 2 - 5 cos x at (0 , - 5). Find any points on the curve x 2 y - xy 2 = 2 where the tangent line is vertical, that is, where d x d y = 0. (3.8.48). Find the equation of the line tangent to x 2 + y 2 = 4 at ( 2 , 2). Find the equation of the line tangent to x 2 + y 2 = 4 at (2 , 0). What is the diﬀerence between this problem and the last one? Let f ( x ) = ( x + 1) 2 x - 1 . Find f 00 (2). (3.7.16). Deep Space 1 was powered by an ion engine for 678 days. A unique feature of ion en- gines is their ability to continuously provide acceleration. Suppose by day t of its mission, DS1 had travelled x ( t ) = 339 t 2 miles. Find DS1’s average velocity for the ﬁrst ten days, its instantaneous velocity after ten days, its acceleration and its velocity when the ion engine shut oﬀ after 678 days. Make sure you indicate the units of your answer. We know that the (evaluated!) value of the derivative represents the slope of the func- tion at a point. Thus the second derivative tells us the slope of the derivative function at a
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Unformatted text preview: point, but what does this tell us about our original function? If s = 1 2 t 4-5 t 3 + 12 t 2 , ﬁnd the velocity of the moving object when its acceleration is zero. (3.7.29). A point moves along a horizontal coordinate line in such a way that its position at time t is speciﬁed by s = t 3-3 t 2-24 t-6. Here s is measured in centimeters and t in seconds. When is the point slowing down; that is, when is its speed decreasing? (3.7.37). Find y 00 at (2 , 1) if 2 x 2 y-4 y 3 = 4. (3.8.39). The curve x 2-xy + y 2 = 16 is an ellipse centered at the origin and with the line y = x as its major axis. Find the equations of the tangent lines at the two points where the ellipse intersects the x axis. (3.8.47). Show that the hyperbolas xy-1 and x 2-y 2 = 1 intersect at right angles. (3.8.42)....
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## This note was uploaded on 07/17/2008 for the course MATH 151 taught by Professor Any during the Summer '08 term at Ohio State.

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