Finding points of intersection?

Question

i need help finding the 3 points of intersection of f(x)=x^2 and g(x)=2^x

And can you please show how you did it..thank you

Well I know there are 2 positive ones at x=2 and x=4, but according to the graph there is a negative one and i knot know how to find it..is using a graphing calculator the only way?

Answer 1

Find the point(s) of intersection of

f(x) = x²
g(x) = 2^x

This would occur when the equations are equal.

x² = 2^x

I see no easy way to solve this, but by inspection I see.
x = 2

So one point (x,y) = (2,4).

Also, there appear to only be two point of intersection. One when x is positive which we have found and one when x is negative. That one will occur somewhere in the interval

-1 < x < 0

Answer 2

At points of intersection both functions have the same value. You therefore want the points where x^2 = 2^x. I don't think that there is any simple algebraic way to solve this equation so you must use approximate methods. Also I think that you will find that there are only two points of intersection between these functions. The positive one is an integer value of x but not the negative one. Try drawing the curves of these functions first.

Later edit. Sorry , I did miss the second positive point of intersection. My only excuse is doing it too fast.

Answer 3

You are looking for the solutions to the equation x^2 - 2^x = 0

2 and 4 are the positive solutions for x
There's a negative solution too, but the only way I know to find
it offhand is to do it graphically or to use Newton's method of successive approximations. The answer is around -.8