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ppose that the only information we have about a function fis that f(1) = -7 and the graph of its derivative is as shown. y = f'(x) 0 1 (a) Use a linear approximation to estimate f(0.99) and f(1.01),

ppose that the only information we have about a function fis that f(1) = -7 and the graph of its derivative is as shown. y = f'(x) 0 1 (a) Use a linear approximation to estimate f(0.99) and f(1.01),

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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Y NOTES ASK YOUR TEACHER Suppose that the only information we have about a function fis that f(1) = -7 and the graph of its derivative is as shown. y = f'(x) 0 (a) Use a linear approximation to estimate f(0.99) and f(1.01). f(0.99) f(1.01) Enter a number. (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 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. O 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. 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. Submit Answer E 3.10 Linearization - linear approximatio... Watch It Player | Ce.... F1 F3 F4 F5 www Tab N Esc 1 Q C @ 2 F2 W #m 3 E $ 4 R % сторо 5 IT < 6 F6 & 7 F7 * * 8 hp FB 9
Transcribed Image Text:Y NOTES ASK YOUR TEACHER Suppose that the only information we have about a function fis that f(1) = -7 and the graph of its derivative is as shown. y = f'(x) 0 (a) Use a linear approximation to estimate f(0.99) and f(1.01). f(0.99) f(1.01) Enter a number. (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 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. O 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. 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. Submit Answer E 3.10 Linearization - linear approximatio... Watch It Player | Ce.... F1 F3 F4 F5 www Tab N Esc 1 Q C @ 2 F2 W #m 3 E $ 4 R % сторо 5 IT < 6 F6 & 7 F7 * * 8 hp FB 9
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