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Consider the function y = g(x) = -x² +3. Use the limit definition of the derivative to compute a formula for y = g'(x). -2x Determine the slope of the tangent line to y = g(x) at the value z = 2 -4 Compute g(2). 9(2) = 7 Find an equation for the tangent line to y = g(x) at the point (2, g(2)). Hint: Use the slope you found above, along with the ordered pair that goes with a = 2. -4(x-2) On the axes provided sketch an accurate, labeled graph of y = g(x) along with its tangent line at the point (2, g(2)). 5 4 3- 2- -7-6-5-4-3-2-1 Clear All Draw: H -1 -2- -3- -4 -5 1 2 3 4 5 6 7

Consider the function y = g(x) = -x² +3. Use the limit definition of the derivative to compute a formula for y = g'(x). -2x Determine the slope of the tangent line to y = g(x) at the value z = 2 -4 Compute g(2). 9(2) = 7 Find an equation for the tangent line to y = g(x) at the point (2, g(2)). Hint: Use the slope you found above, along with the ordered pair that goes with a = 2. -4(x-2) On the axes provided sketch an accurate, labeled graph of y = g(x) along with its tangent line at the point (2, g(2)). 5 4 3- 2- -7-6-5-4-3-2-1 Clear All Draw: H -1 -2- -3- -4 -5 1 2 3 4 5 6 7

Advanced Engineering Mathematics
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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Consider the function y = g(x) = -x² +3. Use the limit definition of the derivative to compute a formula for y = g'(x). -2x Determine the slope of the tangent line to y = g(x) at the value x = 2 -4 Compute g(2). g(2) = 7 Find an equation for the tangent line to y = g(x) at the point (2, g(2)). Hint: Use the slope you found above, along with the ordered pair that goes with a = 2. y = -4(x-2) On the axes provided sketch an accurate, labeled graph of y = g(x) along with its tangent line at the point (2, g(2)). 6 5 Clear All Draw: -7 -6 -5 -4 -3 -2 -1 4 3 2 1 -2 -3- -4 -5 1 2 3 4 5 6
Transcribed Image Text:Consider the function y = g(x) = -x² +3. Use the limit definition of the derivative to compute a formula for y = g'(x). -2x Determine the slope of the tangent line to y = g(x) at the value x = 2 -4 Compute g(2). g(2) = 7 Find an equation for the tangent line to y = g(x) at the point (2, g(2)). Hint: Use the slope you found above, along with the ordered pair that goes with a = 2. y = -4(x-2) On the axes provided sketch an accurate, labeled graph of y = g(x) along with its tangent line at the point (2, g(2)). 6 5 Clear All Draw: -7 -6 -5 -4 -3 -2 -1 4 3 2 1 -2 -3- -4 -5 1 2 3 4 5 6
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