1. Determine the average rate of change between the points x₁ = -4 and x₂ = 4 in the function f(x) = x² 2. Determine the average rate of change between the points x₁ = 0 and x2 = 10 in the function f(x) = 3x² + 3x + 1. 3. Consider the function f(x) = 3x2-16. Using the difference quotient for tangent lines, determine the instantaneous rate of change at the point x = -1 by choosing the following values for h a) h=1 b) h = 0.1 c) h = 0.01 4. Comment on your results in parts a to c above. Which value of h gives you the best estimate of the instantaneous rate of change at the point x = -1? Why? What can you do to get an even better estimate of the instantaneous rate of change at the point x = -1 5. Find the value of the instantaneous rate of change for each of the following functions. a g(x) = x² + 7x, x=2 b. h(x) = x³ -x, x=0
1. Determine the average rate of change between the points x₁ = -4 and x₂ = 4 in the function f(x) = x² 2. Determine the average rate of change between the points x₁ = 0 and x2 = 10 in the function f(x) = 3x² + 3x + 1. 3. Consider the function f(x) = 3x2-16. Using the difference quotient for tangent lines, determine the instantaneous rate of change at the point x = -1 by choosing the following values for h a) h=1 b) h = 0.1 c) h = 0.01 4. Comment on your results in parts a to c above. Which value of h gives you the best estimate of the instantaneous rate of change at the point x = -1? Why? What can you do to get an even better estimate of the instantaneous rate of change at the point x = -1 5. Find the value of the instantaneous rate of change for each of the following functions. a g(x) = x² + 7x, x=2 b. h(x) = x³ -x, x=0
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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Transcribed Image Text:1. Determine the average rate of change between the points x₁ = -4 and x₂ = 4 in the function f(x) = x²
2. Determine the average rate of change between the points x₁ = 0 and x₂ = 10 in the function
f(x) = 3x² + 3x + 1.
3. Consider the function f(x) = 3x2-16. Using the difference quotient for tangent lines, determine the
instantaneous rate of change at the point x = -1 by choosing the following values for h:
a) h=1
b) h = 0.1
c) h = 0.01
4. Comment on your results in parts a to c above. Which value of h gives you the best estimate of the
instantaneous rate of change at the point x = -1? Why? What can you do to get an even better estimate of
the instantaneous rate of change at the point x = -1
5. Find the value of the instantaneous rate of change for each of the following functions.
a g(x)=x² + 7x, x=2
b. h(x)=x²-x, x=0
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