V6 5V6 5Select an appropriate graph of a twice-differentiable function y=f(x) that passes through the points (-V2,1),| --.(0,0),3 '93 '9and (V2 ,1), and whose first two derivatives have the following sign patterns.12V6V633OA.ов.Oc.OD.Ay1854Ay18--33-18

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Answered: V6 5 V6 5 Select an appropriate graph…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = xy + 3 x + 9 y critical point (x, y) = classification Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum valuerelative maximum value
Hint: Find all critical point (m sub 0, b sub 0) and apply Second Derivative Test.
Demonstrate the use of the method with reflections on the use of numerical methods, find the minimum for the function below: F(x,y)= Ax^2 - Bxy- cy^2= x -y (Xo=4, Yo=4) A=2 B=-2 C=1 Identify the minimum again using the Newton’s method with dynamic . However, use this time numerical derivatives instead of . When using numerical derivatives, only one of the constants is being varied as with partial derivatives. Apply in this case the forward numerical derivative, . Here equals some very small number. For each step , solve first the and optimal using the condition . When taking the derivative of , please remember to consider the inner derivatives for each of the coordinate axes that results as dot product with the main function. In this work it is enough that only the second term in the dot product is analyzed using numerical derivatives. Thus, the function takes the form .
consider a continuous function y = f(x) whose first derivative is y = x(x – 2). The function f has a local/relative minimum value when x = choices: a. 2 b. 1 c. 0 d. -2
identify any extrema of the function by recognizing its given form or its form after completing the square. Verify your results by using the partial derivatives to locate any critical points and test for relative extrema. f(x,y) = −x2 − y2 + 10x + 12y − 64
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Find the differential eqn. of the ff. family of curves: a.) Straight lines with slope half the value of the x-intercept b.) Circles with center on the y-axis c.) Circles with center on the line y = x, and passing through the origin
From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)
We have two approaches to classifying critical points as local minima or maxima: the first derivative test and the second derivative test. In what situations is the second derivative test easier to use than the first?
Identify any extrema of the function by recognizing its given form or its form after completing the square. Verify your results by using the partial derivatives to locate any critical points and test for relative extrema. g(x, y) = (x − 4)2 + (y − 3)2
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V6 5 V6 5 Select an appropriate graph of a twice-differentiable function y=f(x) that passes through the points (-V2,1) , - 3 '9 (0,0), 3 '9 and (V2 ,1), and whose first two derivatives have the following sign patterns. 12 V6 V6 3 3 OA. в. Oc. OD. Ay 18 54 Ay 18- -3 3. 3 -18