Consider the differebtiable function F(z) with known values given in the table below. I 1.00 F(1) 4.00 1.40 1.80 2.20 2.60 3.00 4.96 6.24 .84 9.76 12.00 (a) List all possible estimates for the slope of F(z) at z = 3.40. 3.40 14.56 If the estimation formula applies enter below your answers round to two decimal places. Otherwise enter NA. (b) Estimate for the value of F(1) round to two decimal places. F' (1) Number 3.80 17.44 Forward Difference Estimate Backward Difference Estimate Central Difference Estimate Number Number Number 4.20 20.64 F'(4.2) Number (c) Estimate the value of the instantaneous rate of change of F(z) at z = 4.2 round to two decimal places.
Consider the differebtiable function F(z) with known values given in the table below. I 1.00 F(1) 4.00 1.40 1.80 2.20 2.60 3.00 4.96 6.24 .84 9.76 12.00 (a) List all possible estimates for the slope of F(z) at z = 3.40. 3.40 14.56 If the estimation formula applies enter below your answers round to two decimal places. Otherwise enter NA. (b) Estimate for the value of F(1) round to two decimal places. F' (1) Number 3.80 17.44 Forward Difference Estimate Backward Difference Estimate Central Difference Estimate Number Number Number 4.20 20.64 F'(4.2) Number (c) Estimate the value of the instantaneous rate of change of F(z) at z = 4.2 round to two decimal places.
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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Transcribed Image Text:Consider the differebtiable function F(z) with known values given in the table below.
I
1.00
F(1) 4.00
1.40
1.80 2.20 2.60 3.00
4.96 6.24 .84 9.76 12.00
(a) List all possible estimates for the slope of F(z) at z = 3.40.
3.40
14.56
If the estimation formula applies enter below your answers round to two decimal places. Otherwise enter NA.
(b) Estimate for the value of F(1) round to two decimal places.
F' (1) Number
3.80
17.44
Forward Difference Estimate Backward Difference Estimate Central Difference Estimate
Number
Number
Number
4.20
20.64
F'(4.2) Number
(c) Estimate the value of the instantaneous rate of change of F(z) at z = 4.2 round to two decimal places.
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Step 1: We first determine what is given and which formula we are going to use.
VIEWStep 2: slope at a point on a differentiable function is given by derivative so we find derivative of F(x)
VIEWStep 3: For (b) we use Forward difference estimate and for (c) we use backward difference estimate
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