00:01
In this question, we are given a function fx which is equals to x to the power 4 plus 6x cube minus 18x square.
00:13
Using intermediate value theorem, we have to show that there exists a real zero between x equals to 2 and x equals to 3.
00:48
So, what do we mean by the question? we mean that for some x there exists some x for which f of x is equals to 0 where x belongs to the domain 2 ,3.
01:17
Using intermediate value theorem, we have to show this.
01:21
Now, we will use the properties of continuity and continuous functions in this question.
01:39
Every polynomial function is a continuous function.
01:46
So, this function is also continuous.
01:48
This implies if a function is continuous, we have x axis over here and y axis over here.
01:58
If a function is continuous like this, we have something in our domain c and we have another point x.
02:10
So, it has to take all the values.
02:16
These are all the values of y that correspond to all the values that we get between c and d.
02:24
So, if this is our domain, then we get all the values between f of c and f of d.
02:38
So, we get all the values.
02:42
Here we have something f of c and here we have f of d.
02:51
This is a property of continuous functions.
02:53
So, given question we have f of 2 will be 2 to the power 4 plus 6 times 2 to the power 3 minus 18 times 2 to the power 2 which is 16 plus 48 minus 72.
03:09
This value will be minus 8...
