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Suppose that the only Införmation we have ab8ut a fuRcEiOH FIS y= f'(x) (a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) = (1.1) =

Suppose that the only Införmation we have ab8ut a fuRcEiOH FIS y= f'(x) (a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) = (1.1) =

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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Suppose that the only information we have about a function f Is that f(1) = -7 and the graph of its derivative is as shown. y=f'x) -1 01 1 (a) Use a linear approximation to estimate f(0.9) and (1.1). f(0.9) = f(1.1) = (b) Are your estimates in part (a) too large or too small? Explain. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too small. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too large. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too small.
Transcribed Image Text:Suppose that the only information we have about a function f Is that f(1) = -7 and the graph of its derivative is as shown. y=f'x) -1 01 1 (a) Use a linear approximation to estimate f(0.9) and (1.1). f(0.9) = f(1.1) = (b) Are your estimates in part (a) too large or too small? Explain. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too small. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too large. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too small.
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