*t = m ∂f/∂x*

When,

*is at zero and***x***is***m***0.00024*. The experimental data is given for the function*at four different points of***f***.***x****|**

*x**0 | 1 | 2 | 3*

----------------------------------------------

*|*

**f***0 | 55.56 | 88.89 | 100*

Plotting the values of

*with respect to***f***gives following graph:***x**

Our goal is to find the value of

*by fitting the given experimental data through a polynomial. The most general***t***nth*degree polynomial is,

*Pₙ (x) = aₒ + a₁ x + a₂ x² + a₃ x³ + ... .... ... + aₙ xⁿ*

Where,

*aₒ*,*a₁,**a₂,**a₃, ... ...**aₙ*are constant coefficients of the polynomial equation. As it is mentioned in the experimental data where the function values are known for four respective points, so a third degree polynomial would fit the data. The third degree polynomial is,

*f (x) = aₒ + a₁ x + a₂ x² + a₃ x³*Where, the coefficients are to be determined. According to the experimental data, we have,

*f (0) = aₒ + a₁ (0) + a₂ (0)² + a₃ (0)³*

⇒

*aₒ = 0*

Then,

*f (1) = aₒ + a₁ (1) + a₂ (1)² + a₃ (1)³*

⇒

*a₁ +**a₂ +**a₃**= 55.56*.....................................................(1)Then,

*f (2) = aₒ + a₁ (2) + a₂ (2)² + a₃ (2)³*

⇒ 2

*a₁ + 4**a₂ + 8**a₃**= 88.89*.............................................(2)Then,

*f (3) = aₒ + a₁ (3) + a₂ (3)² + a₃ (3)³*

⇒ 3

*a₁ + 9**a₂ + 27**a₃**= 100*...............................................(3)Now, from equation (1):

*a₁**= 55.56 -*

*a₂ -*

*a₃*

Substituting

*a₁*into equation (2):

*a₂ + 3**a₃ = -11.115*..............................................................(4)

Again, substituting

*a₁*into equation (3):

*a₂ + 4**a₃ = -11.113*..............................................................(5)

Subtracting equation (5) from (4), we have,

*a₃ = 0.002*

Now, substituting

*a₃*in equation (4), we get,

*a₂ = - 11.121*

And finally we get,

*a₁**= 66.679*

So, our polynomial function is,

*f (x) =**66.679*

*x*

*- 11.121*

*x² +**0.002*

*x³*

A plot is obtained to visualize the approximated function’s shape for the corresponding values of

**where function values are determined for***x***x**, which is started from*0*with an interval*0.005*between points until*3*. Following figure shows a smooth graph compared to the aforementioned one.Now, we can determine the value of ∂f/

*∂x*:

*∂f/∂x =**66.679*

*- 22.242*

*x +**0.006*

*x²*

At

*x = 0*, we get,

*∂f/∂x =**66.679*

Now, to evaluate

**, according to the given equation:***t*

*t = m ∂f/∂x*

*t = 0.00024 ×**66.679 = 0.016*

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