solve problems involving partial derivatives (TLO8)no. 1 a²zB. For each of the following functions z, finda²za²zandду?дхz дудх' дхду'1. z %3D 2x2 — 5ху + у?-2. z= sin3x cos4y3. z = tan-1 (2)

Answered: Image /qna-images/answer/a6d45c53-80bd-4085-b6f8-25b39c955eda.jpg

Answered: a²z B. For each of the following…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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QUESTION 3 Find the second order partial derivative Y (x,z) xXZ of the function Y= 10 Y (x,z) = - XZ Z Y (x,z) = XZ Y (x,z) = XZ Y (x,z) = XZ x 3 20 10 x2 10z x2 -20 x 3
-5 -4 -3 -2 -1 6 4 3 2 1 Ń -3 -4 2 3 St Use the graph of f(x) above to estimate the value of f'(0) to one decimal place. ƒ'(0)
Let P(t) represent the price of a share of stock of a corporation at time t. What does each of the following statements tell us about the signs of the first and second derivatives of P(t)? (Hint - you might want to sketch a possible graph.) (a) The price of the stock is rising faster and faster. The sign of dP dt is ---Select--- v The sign of (b) The price of the The sign of The sign of d²p dt² is --Select--- ✓ stock is close to bottoming out. dP dt d²p dt² is ---Select--- ✓ is ---Select--- ✓
Question 11 Suppose 8 (x) x++1. What is the correct result of the second derivative of g with respect to x? x²+1 A 8"(x) = (x²+ 1)² x²Vx²+1 (x²+ 1)2 B 8"(x) = (x²– 1) /x²+ 1 (x²+ 1) ² g"(x) = - D - 8"(x) = *Vx²+1 x2+1
(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
5.2(4) PLEASE SHOW YOUR WORK STEP BY STEP THANK YOUUU :)) Calculates the second derivative of the function (shown in the image) Determines the intervals on which the graph of the Function is concave upwards and the intervals on which it is concave downwards.
5-2 Compute the derivative ficts of the logistic sigmoid 1 fax= H 50 1 + exp(-x) 0.
3. Explain two different ways to solve for the derivative of s(0) = -5cote and show all steps for each method. (Hint: They are both similar but require different derivative rules.) a) Method 1 b) Method 2 [C/4] [C/4]
4. D11: I can use derivatives to solve optimization problems. (a) Part of the graph of f(x) = x + 2x is given below. i. Does the graph indicate that x = 0 is a critical point? Why/Why not? ii. Use calculus and algebra to find all possible x values where f could possibly change direction (change from increase to decrease or vice versa). Does your algebra indicate that x = 0 is a critical point? Why/Why not? lasif (b) Use the first derivative test to show that f does not have a maximum or a minimum at x = 0. (Hint: you may need to look up this test. Show why it is ok to apply the test to this situation.)

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a²z B. For each of the following functions z, find a² z and ду? a² z дх? дудх" дхду" 1. z = 2x2 – 5xy + y² 2. z= sin3x cos4y -