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EBK CALCULUS EARLY TRANSCENDENTALS SING
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- The equation below defines y implicitly as a function of x: 2x2 + xy = 3y2 Use the equation to answer the questions below. A) Find dy/dx using implicit differentiation. SHOW WORK. B) What is the slope of the tangent line at the point (1, 1)? SHOW WORK. C) What is the equation of the tangent line to the graph at the point (1, 1)? Put answer in the form y = mx + b and SHOW WORK.arrow_forwardFind the derivative of the function at the given point in the direction of A. f(x, y) = -10x2 + 5y, (-9,10), A=31-4j O 212 104 176 140 さ0000arrow_forwardFind the derivative of the function f(x,y) = x+ xy + y at the point (5,6) in the direction in which the function decreases most rapidly. O A. - 545 O B. - 461 O C. -3/62 O D. -V455 Click to select your answer. a 61) archarrow_forward
- Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 2² + y? = (2x² + 2y² -a)°, (0, 1/2) (cardioid) X y = Subrait aecue 888 4) FZ F9 %23 2$ % & 5 6 9 delete E R Y F J K V B N command optionarrow_forwardUse the contour diagram of ƒ to decide if the specified directional derivative is positive, negative, or approximately zero. 1. At the point (0, 2) in the direction of 7, 2. At the point (−1, 1) in the direction of ? ? (−i +j)/√2, ? (i - 2j)/√5, ? (-i-j)/√2, ? ? 3. At the point (0, −2) in the direction of 4. At the point (-1, 1) in the direction of 5. At the point (-2, 2) in the direction of i, 6. At the point (1, 0) in the direction of -j, 2.4 1.6 0.8 0 -0.8 -1.6- -2.4 12.0 12.0 10.0 6.0 10.0 -2.4 -1.6 -0.8 0 X 0.8 4.0 1.6 12.0 10.0 8. 10.0 12.0 2.4 (Click graph to enlarge)arrow_forwardUse implicit differentiation to find y′.Then evaluate y′ at (−2,0). -32ey=x5-y5 y′= 5x4/5y4-32ey How did they get this?arrow_forward
- sketch the curve ƒ(x, y) = c together with ∇ƒ and the tangent line at the given point. Then write an equation for the tangent line. x2 + y2 = 4, (sqrt(2), sqrt(2))arrow_forwardV= (1,2,2). What is the derivative of the direction?arrow_forwardEvaluate the derivatives of the following functions using implicit differentiation. Simplify.arrow_forward
- Considering the following graph of the given function f. у The xy-coordinate plane is given. The curve enters the window in the second quadrant nearly horizontal, goes down and right, crosses the negative x-axis, changes direction on the negative y-axis, goes up and right, crosses the positive x-axis, and exits the window in the first quadrant nearly horizontal. Use the graph of f to complete the following table. f(x) f'(x) x > 0 f(x) > 0 f'(x) ? v 0 x > 0 f(x) 0 f'(x) ? v 0 x < 0 f(x) < 0 f'(x) ? v 0 Sketch the graph of f and f' on the same coordinate axes. y y yarrow_forwardCalculate the derivative of the function. Then find the value of the derivative as specified. dr de e =3 ifr = 28-e Select one: e =3 4 A. dr = - de (28– e)3/2 de 125 dr |8 =3= 4 B. dr = de (28- e)3/2 de 4. 125 e =3 2 C. dr = - de dr (28 - e)3/2 de 2 = - 125 2 e =3 dr '= 2 D. dr = de (28 - e)3/2 de 125arrow_forwardShow the step by step process.arrow_forward
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning