(a) Use a linear approximation to estimate f(0.99) and f(1.01). f(0.99) = 1.98 f(1.01) 2.02 (b) Are your estimates in part (a) too large or too small? Explain. 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. 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 positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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I guess I really had no idea how to do this since they are all wrong. Need help.

Suppose that the only information we have about a function f is that f(1) = -2 and the graph of its derivative is as shown.
y3 f'(x)
0.
(a) Use a linear approximation to estimate f(0.99) and f(1.01).
F(0.99) 1.98
f(1.01) 2.02
(b) Are your estimates in part (a) too large or too small? Explain.
O 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.
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 positive, but the tangents are becoming less steep. So the tangent lines lie
above the curve f. Thus, the estimates are too large.
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Transcribed Image Text:Suppose that the only information we have about a function f is that f(1) = -2 and the graph of its derivative is as shown. y3 f'(x) 0. (a) Use a linear approximation to estimate f(0.99) and f(1.01). F(0.99) 1.98 f(1.01) 2.02 (b) Are your estimates in part (a) too large or too small? Explain. O 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. 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 positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large. Need Help? Read It Watch It
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