Compare functions

Question

Compare the functions f(x) = x^7 and g(x) = 7^x  by graphing both functions in several viewing rectangles. Find all points of intersection of the graphs correct to one decimal places

smaller x-value (x, y) =

larger x-value (x, y) =

Answer 1

It is actually easier to graph h(x) = 7^x - x⁷ and locate where "h" crosses the x-axis. One obvious root is 7 because 7⁷ = 7⁷.

Check out:

desmos.com/calculator/ujjitoh0go

to see the other possible value of x that makes these two functions equal.

Here is another Desmos graph that uses Newton's method to calculate the smaller root.

desmos.com/calculator/v8yafohpxc