Three point formula exercise question

Question

Using the table in the figure and the three point formula find the approximate values of the derivative required f'(1.2).Also calculate Ea and Ev ( Actual error and error bound) enter image description here

We notice that h=0.1

so f'(1.2)=[1/(2*0.1)]* [f(1.3)-f(1.1)] Is this correct?

How to find Ea and Ev now?

score 3 · Accepted Answer · answered Feb 11 '15 at 16:23

3

I will map it out and you can fill in the details.

To find the derivative, we use:

$$f'(x) = \frac{f(x + h) - f(x - h)}{2h} - \frac{h^2}{6} f^{(3)}(\xi_0)$$

where $\xi_0 \in (x-h, x+h)$.

For your problem:

$$\tag 1 f'(1.2) = \frac{f(x + h) - f(x - h)}{2h} = \frac{f(1.3) - f(1.1)}{2 \times 0.1}$$

The error bound will be given by:

$$\mbox{Max}~ \left|- \frac{h^2}{6} f^{(3)}(\xi_0)\right|, \xi_0 \in (x-h, x+h)$$

The actual error will be given by:

$$|\mbox{Actual value} - \mbox{Calculated value from}~(1)|$$

answered Feb 11 '15 at 16:23

Amzoti

56,093

Actual error is Ev right? – user3543012 Feb 11 '15 at 18:57
I will solve this and post the answers to compare them with yours – user3543012 Feb 11 '15 at 18:57
So f'(1.2) is 22.19365, Error bound is 0.17951650713 – user3543012 Feb 11 '15 at 19:36
What is an actual value? – user3543012 Feb 11 '15 at 19:39
For the actual value, take the derivative of the known $f(x) = e^{2x}$ and evaluate it at $x = 1.2$, correct on error bound, correct on numerical derivative calculation. – Amzoti Feb 11 '15 at 19:42
Actual error =Ev= |-0.147| – user3543012 Feb 11 '15 at 20:07
That is correct. – Amzoti Feb 11 '15 at 21:10

Three point formula exercise question

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