Quiz 10(Prequiz)-Implicit Differentiation 1

Quiz 10(Prequiz)-Implicit Differentiation 1 - Calculus...

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Unformatted text preview: Calculus Prequiz 10 - Implicit Differentiation Name___________________________________ Date______________________ Objective: You will be able to determine the derivative of a curve using implicit differentiation You will be able to determine the slope and equations of the tangents to a curve using implicit differentiation SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find dy/dx by implicit differentiation. If applicable, express the result in terms of x and y. 1) 8x + 5y = 9 2) 4y - 7x2 = x - 8 3) 4y2 - 7x2 - 15 = 0 4) 7y + 3xy - 9 = 0 Find dy/dx by implicit differentiation. 5) x3 + 3x 2 y + y 3 = 8 1 At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as requested. 6) x2 + y2 - 2x + 4y = 8, tangent at (4, 0) Find the requested slope, tangent, or normal at the indicated point on the given curve. 7) y4 + x3 = y2 + 12x, slope at (0, 1) 8) x5 y5 = 32, slope at (2, 1) Solve the problem. 9) Find the slope of the curve xy3 - x5 y2 = -4 at (-1, 2). 10) Find the points on the curve x2 - xy + y2 = 12 where the tangent is parallel to the x-axis. 2 Answer Key Testname: QUIZ 10IMPLICIT DIFFERENTIATION 1 1) - 2) 3) 4) 8 5 1 + 14x 4 7x 4y -3y 7 + 3x x2 + 2xy x2 + y 2 5) - 3 6) y = - (x - 4) 2 7) 6 8) - 9) - 1 2 3 2 10) (-2, -4), (2, 4) 3 ...
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