- The Derivative Of A Function Can Be Used To Calculate The Slope Of The Function At A Given Point However The Slope Of 1 (235.92 KiB) Viewed 79 times
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(x₁+1)-f(x₂) slope = X+1-N₂ 10 X=3 Xi+1 = 2 9 8 7 6 5 4 3 2 1 0 -f(x) -slope at x 1 approx. of slope 0.5 1 (1,f(1)) 1.5 X 2 (2,1(2)) 2.5 3 (3,f(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. slope apprx = 4 slopex=3 As the increment between the two points, inc=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 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. Find the slope of the following equation at the point specified using the approximation method. 5x² log (7.x²) Start with an increment of 1, and reduce the increment by half until the two consecutive approximations are within 0.01% of each other.