Using Excel VBA code to create this program:

3) This problem will have you program a very basic numerical differentiation. (x - h/2) (x + h/2) To calculate a numerical derivative, first a value ofx is chosen (the location where the derivative will be calculated). A secant line is drawn that intersects the function at two placesffr +h/2) and ffix - h/2), and these two function bracket the x value. The derivative is calculated as the slope of this line dx As shown in the figure, the value calculated from this method will be different than the actual derivative. However, as the distance h decreases in magnitude, the value of the derivative will become closer to the actual value Write a program that calculates the numerical derivative of the following function For this problem: Input values for x and the tolerance from theA spreadsheet. 1 tolerance0.001 1.22 Run Calculate the tolerance beginning with the second derivative calculation. For this e is the magnitude of the 4 iteration dy/dx tolerance difference between successive derivative calculations. Iterate until the tolerance is below the threshold entered in the spreadsheet Use a single function to calculate f(x). This 8 1 17.96678 210.64678 3 8.816784 7.32 1.83 8.359284 0.4575 8.244909 0.114375 6 8.216315 0.028594 7 8.209167 0.007148 8 8.20738 0.001787 9 8.206933 0.000447 nction will be called twice per iteration when calculating f(+) and f (x) Test your program with a function you can take the derivative analytically (through calculus) 10 12 Submit a validation of your program. 14 3) This problem will have you program a very basic numerical differentiation. (x - h/2) (x + h/2) To calculate a numerical derivative, first a value ofx is chosen (the location where the derivative will be calculated). A secant line is drawn that intersects the function at two placesffr +h/2) and ffix - h/2), and these two function bracket the x value. The derivative is calculated as the slope of this line dx As shown in the figure, the value calculated from this method will be different than the actual derivative. However, as the distance h decreases in magnitude, the value of the derivative will become closer to the actual value Write a program that calculates the numerical derivative of the following function For this problem: Input values for x and the tolerance from theA spreadsheet. 1 tolerance0.001 1.22 Run Calculate the tolerance beginning with the second derivative calculation. For this e is the magnitude of the 4 iteration dy/dx tolerance difference between successive derivative calculations. Iterate until the tolerance is below the threshold entered in the spreadsheet Use a single function to calculate f(x). This 8 1 17.96678 210.64678 3 8.816784 7.32 1.83 8.359284 0.4575 8.244909 0.114375 6 8.216315 0.028594 7 8.209167 0.007148 8 8.20738 0.001787 9 8.206933 0.000447 nction will be called twice per iteration when calculating f(+) and f (x) Test your program with a function you can take the derivative analytically (through calculus) 10 12 Submit a validation of your program. 14