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HW Supplement: Equation of Tangent Line 1. Let f(x)=0.1x³-2.5x+3.4 Name a). Use a graphing tool to graph of f(x) for the window x[-6,6] and y[-5,10] and find f(0), (6), and (4). Then plot and label the three points and reproduce a sketch of the graph below. 15 b. Use a ruler to sketch, above, the secant line between the points where x = 0 and x = 6. The slope of this secant line is the AVERAGE rate of change of f(x) over the interval [0,6]. c. Find the average rate of change of f(x) over the interval [0,6]. (show work). d. Use a ruler to sketch, above, the tangent line to f(x) at the point where x = 4. e. Is the slope of the tangent line greater or less than the slope of the secant line drawn? (guess) f. Use the basic rules to find f'(x). f(x)=0.1x³-2.5x+3.4 f'(x)= The instantaneous rate of change off at x= 4 is the slope of the tangent line at that point. The slope of the tangent to a function at a point is the derivative at that point. g. Find f'(4) = and compare this slope to the slope of the secant from (c). h. Use your results in part g to find the equation of the tangent line to f(x) at x = 4. Pt: (4, f(4)) Slope: m = f'(4) Equation of line: y-y=m(x-x) (over)

HW Supplement: Equation of Tangent Line 1. Let f(x)=0.1x³-2.5x+3.4 Name a). Use a graphing tool to graph of f(x) for the window x[-6,6] and y[-5,10] and find f(0), (6), and (4). Then plot and label the three points and reproduce a sketch of the graph below. 15 b. Use a ruler to sketch, above, the secant line between the points where x = 0 and x = 6. The slope of this secant line is the AVERAGE rate of change of f(x) over the interval [0,6]. c. Find the average rate of change of f(x) over the interval [0,6]. (show work). d. Use a ruler to sketch, above, the tangent line to f(x) at the point where x = 4. e. Is the slope of the tangent line greater or less than the slope of the secant line drawn? (guess) f. Use the basic rules to find f'(x). f(x)=0.1x³-2.5x+3.4 f'(x)= The instantaneous rate of change off at x= 4 is the slope of the tangent line at that point. The slope of the tangent to a function at a point is the derivative at that point. g. Find f'(4) = and compare this slope to the slope of the secant from (c). h. Use your results in part g to find the equation of the tangent line to f(x) at x = 4. Pt: (4, f(4)) Slope: m = f'(4) Equation of line: y-y=m(x-x) (over)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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HW Supplement: Equation of Tangent Line 1. Let f(x)=0.1x³-2.5x+3.4 Name a). Use a graphing tool to graph of f(x) for the window x[-6,6] and y[-5,10] and find f(0), (6), and (4). Then plot and label the three points and reproduce a sketch of the graph below. 15 b. Use a ruler to sketch, above, the secant line between the points where x = 0 and x = 6. The slope of this secant line is the AVERAGE rate of change of f(x) over the interval [0,6]. c. Find the average rate of change of f(x) over the interval [0,6]. (show work). d. Use a ruler to sketch, above, the tangent line to f(x) at the point where x = 4. e. Is the slope of the tangent line greater or less than the slope of the secant line drawn? (guess) f. Use the basic rules to find f'(x). f(x)=0.1x³-2.5x+3.4 f'(x)= The instantaneous rate of change off at x= 4 is the slope of the tangent line at that point. The slope of the tangent to a function at a point is the derivative at that point. g. Find f'(4) = and compare this slope to the slope of the secant from (c). h. Use your results in part g to find the equation of the tangent line to f(x) at x = 4. Pt: (4, f(4)) Slope: m = f'(4) Equation of line: y-y=m(x-x) (over)
Transcribed Image Text:HW Supplement: Equation of Tangent Line 1. Let f(x)=0.1x³-2.5x+3.4 Name a). Use a graphing tool to graph of f(x) for the window x[-6,6] and y[-5,10] and find f(0), (6), and (4). Then plot and label the three points and reproduce a sketch of the graph below. 15 b. Use a ruler to sketch, above, the secant line between the points where x = 0 and x = 6. The slope of this secant line is the AVERAGE rate of change of f(x) over the interval [0,6]. c. Find the average rate of change of f(x) over the interval [0,6]. (show work). d. Use a ruler to sketch, above, the tangent line to f(x) at the point where x = 4. e. Is the slope of the tangent line greater or less than the slope of the secant line drawn? (guess) f. Use the basic rules to find f'(x). f(x)=0.1x³-2.5x+3.4 f'(x)= The instantaneous rate of change off at x= 4 is the slope of the tangent line at that point. The slope of the tangent to a function at a point is the derivative at that point. g. Find f'(4) = and compare this slope to the slope of the secant from (c). h. Use your results in part g to find the equation of the tangent line to f(x) at x = 4. Pt: (4, f(4)) Slope: m = f'(4) Equation of line: y-y=m(x-x) (over)
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