Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 11.2, Problem 31PS
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22
9. What is the equation of the line tangent to the graph of the function f at the point (1,1)?
f (x) = x2
y =
= 2x – 1
O y = 2x + 1
O y = 2x – 3
O y = 2x + 3
43. Show that f(x) = x² - 7x² − 8x − 3 has exactly one criti-
-
cal point c in the interval (2, 3).
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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- 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.arrow_forward19. Suppose g is a differentiable function for all real numbers. Given that g(x) dx 12 and (g(x) + 3) dx = 7, what is the value of (g(x)+5) dx? (A) 5 (B) 14 () 20 (D) 26arrow_forward39. If f and g are functions defined by f (x, y, z) = (x, 0, z) and g(x, y, z) = (x, z, 'y); then 8(f (0, y, z)) = (A) (0, z, 0) (B) (0, y, 0) (C) (0,0, 0) (D) (x, z, 0) (E) (x, y, 0)arrow_forward
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