math
posted by sonya on .
x^34x2 [2,3]
we have to use the intermediate value thereom. not sure how to do this.

x^34x2 [2,3]
the function is continuous between 2 and 3
at 2 f(2) = 2
at 3 f(3) = +13
The theorem states that for every number N between 2 and +13, there is some x between 2 and 3 such that f(x) = N
Now they did not give you an N so I will say 5 for example is between 2 and +13
The theorem says that some x between 2 and 3 will come out with f(x)= 5
I would have to solve it by trial and error but I know to start between 2 and 5
x f(x)
2 2
try 2.5 > 3.63 too small
try 2.7 > 6.88 too big
try 2.6 > 5.18 closer, a bit big
try 2.58 > 4.85 a little small
try 2.585> 4.93 well you get the idea
3 13
The theorem says that