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Directional DerivativeConsider the function
and the unit
Does the directional derivative of
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Chapter 13 Solutions
Calculus (MindTap Course List)
- Sign of VelocityWhen directed distance is decreasing, is velocity positive or negative? What is the velocity when directed distance is not changing?arrow_forwardVelocity What is the rate of change in directed distance?arrow_forwardThe domain of the function f(x,y) =, ху is V x² + y? The upper half plane without the origin The second and the fourth quadrant without the origin The first and the third quadrant without the origin The left right plane without the originarrow_forward
- Marginal Productivity A manufacturer estimates that pro- duction (in hundreds of units) is a function of the amounts x and y of labor and capital used, as follows. 3 f(x, y) = (a) Find the number of units produced when 16 units of labor and 81 units of capital are utilized. (b) Find and interpret f,(16, 81) and f,(16, 81). (c) What would be the approximate effect on production of increasing labor by 1 unit from 16 units of labor with 81 units of capital?arrow_forwardDisplacement Revisited I was driving to a birthday party at my friend's house when I had the realization: I forgot the birthday gift. My velocity at i seconds after the realization is measured in meters per second and given by the function v(t) = 20 – 21, where traveling towards my friend's house is the positive direction. Label Equation/Value Displacement on [0,10] 100 Displacement on [10,20] -100 Fill out the following table to estimate the displacements on the intervals [0,2], [2,4], [4,6], [6,8], and [8,10]. Recall that v(t) = 20 – 21. Oh nol The gtl Friend's House Interval v(a) Displacement Got it? [a,b] [0.2] Кеep trying! [2,4] Кеep trying! My house [4,6] Кeep trying! [6,8] Keep trying! [8.10] Кеep trying! 10 Once your table is correct, enter your approximation for the displacement on the interval [0,10] below. 5 10 15 20 -10 Кeep trying! -20 Graph of my velocity at time tarrow_forwardA function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where a, b and c are real numbers. It is given that the tangent plane to the graph off at the point (−1, 3, ƒ(−1, 3)) has equation z = -6x-y-3. a) Explain why the information given tells you that f(-1, 3) = 0. b) Consider the contour line of the function f through the point (-1, 3) in the (x, y)-plane. Find the equation of the tangent line to this contour line at the point (-1, 3). You do not need to find the values for a, b and c to answer this question! c) Find the values for the numbers a, b and c.arrow_forward
- X The function f is defined by f (x) = - x+4 What point(s) (x, y) on the graph of f have the property that the line tangent to f at (x, y) has slope ? 4 O (0,0) only (1,16) only 5 O (0,0) and (-8,2) ○ (0,0) and (4,1) O There are no such points.arrow_forwardINTEGRAL The curve has a gradient function 2x - 3 and passes through (1,-6). Find the value of x when y = 0 Choices: x = √(165/4) - (1/2) x = √(165/4) + (3/2) None of the choices x = √(165/4) + (1/2)arrow_forwardsec2(0) de V5-sec2(0)arrow_forward
- Use Application of Derivatives A wire of length L is to be cut into two pieces, one to form a square and the other to form an equilateral triangle. How should the wire be divided to maximize or to minimize the sum of the areas of the square and triangle?arrow_forwardMATH • CALCULUS Find the particular anti derivative that satisfies the following conditions: dy/dx=3x+5/sqrt3 of x; y(1)=8 Y=? * sqrt3 of x as in the 3 is in the V of the squareroot but it is x in the squarerootarrow_forwardWhat is the area of the region in the first quadrant, bounded by the curve y = Vx and y = x? (В) 4 (©) ; (A) (D) 2arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning