Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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3. Suppose that the temperature on a metal plate is given by the function T with
T(x, y) = 100 - (x² +4y²)
where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now
suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the
point (1, 4) to the point (5, 6).
(a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6)
in one minute at a constant speed.
(b) What can you say about
dr
dt
and
dy
dt
for every value of t?
(c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi-
encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.
Answer number 4 and 5 pls. I don't want to waste my money here.
Find the derivatives of all orders of the functions
Chapter 11 Solutions
Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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- 5. Find the derivative of the following function. y = In(6x – 7x)-4x A) 18x? – 7x 4 x(6x² – 7) В) 1 4 x(6x² – 7) 18x – 7 -4 x(6x² – 7) C) D) 18x? 4 x(6x - 7) E) 1 4 x(6x² – 1)arrow_forwardSuppose that f has continuous second derivatives, and with critical points at (4, 3), (−4, 3), (−2, −3), (4, −1). Use the information given below to apply the second derivative to each of the points given. ? ? ? ? ♦ 1. fxx(−2, −3) = 16, fyy(−2, -3) = 9, fxy(−2, −3) = 15 2. fxx (4, -1) = 4, fyy(4, −1) = 1, fxy(4, −1) = 2 3. fxx(-4, 3) = 16, fyy(-4, 3) = 9, fay(-4, 3) = 9 4. fxx (4, 3) = −16, fyy(4, 3) = −9, fxy(4,3) = 9arrow_forwardIn substituting the point (4,1,2) in the partial derivatives, why does the terms without x and y becomes zero?arrow_forward
- 3. If f(r, y) = a²y? - 2x-4y, then the total derivative of f %3Darrow_forward6) When some variable z is a function of time (t), the derivative of z with respect to t is denoted using the "dot" notation: * = r(t). If a(t) and b(t) are positive-valued differentiable functions of time (t), and if A, a, and 3 are constants, find expressions for i/x where (a) r(t) = (a(t))² b(t) (b) x(t) = A (a(t))a (b(t)) ³ a+B (c) z(t) =A((a(t))° + (B(t))) aarrow_forwardFor each part of this problem, state whether or not it is possible for a function f of two variables with continuous second partial derivatives to satisfy the given conditions. If it's possible, find such a function f; if it's not possible, explain why. af af (a) sin(y), cos(x) ду af (Ъ) af cos(y) dy sin(x),arrow_forward
- If the derivative of an analytic function f is 0, does that mean that the partial derivative of f with respect to x=0 and the partial derivative of f with respect to y=0? And conversely, suppose I know the partial derivates of a function are both equal to 0, can I then assume that the derivative of the function is 0? Hope this makes sense.arrow_forwarda) Suppose you are given model with two explanatory variables such that: Y₁ = a + B₁x₁i + B₂x₂₁x + u₁, i = 1,2,...n Using partial differentiation derive expressions for the expressions for the intercept and slope coefficients for the model above.arrow_forward
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