Question #2096b
1 Answer
Three solutions are (to 10dp):
# x_1 = -0.3714177525 #
# x_2 = 0.6052671213 #
# x_3 = 4.7079379181 #
Explanation:
Let:
# f(x) = e^x-5x^2 #
Our aim is to solve
graph{e^x-5x^2 [-5, 10, -30, 10]}
We can see that there are three solutions; one solution in the interval
To find the solution numerically, using Newton-Rhapson method we use the following iterative sequence
# { (x_1,=x_0), ( x_(n+1), = x_n - f(x_n)/(f'(x_n)) ) :} #
Therefore we need the derivative:
# \ \ \ \ \ \ \f(x) = e^x-5x^2 #
# :. f'(x) = e^x-10x #
Then using excel working to 10dp we can tabulate the iterations as follows:
Initial Value
Initial Value
Initial Value
We could equally use a modern scientific graphing calculator as most new calculators have an " Ans " button that allows the last calculated result to be used as the input of an iterated expression.
And we conclude that the three solutions are (to 10dp):
# x_1 = -0.3714177525 #
# x_2 = 0.6052671213 #
# x_3 = 4.7079379181 #