Can you help me write the code for this MATLAB assignment? All relevant information can be found in the attached image(s).
The derivative of a function can be used to calculate the slope of the function at a given point. However, the slope of a function at point x can be estimated using the function: f(x+i+1) - f(x+i) / (x+i+1) - (x+i)
f(x) slope at x=1 approx. of slope
3, f(3)
(2, f(2))
1, f(1)
0.5
1.5
2
2.5
3
3.5
As you can see in the figure, the slope at x=1 is 2, but two estimates of the slope using the equation are also shown. (x+1)/3 slope approx -4 (x+1)/2
As the increment between the two points, x-x+1/x, decreases, the slope approximation approaches the true slope. Therefore, if we make the increment small enough, we can get a good approximation of the slope at that point. However, since the increment size required to get a good approximation varies from function to function and even point to point, this method is often implemented in an indefinite loop where the increment is decreased every iteration until two consecutive approximations of the slope are within a given tolerance.
5x^2
y = log(7x)
Start with an increment of 1, and reduce the increment by half until the two consecutive approximations are within 0.01% of each other.
