00:01
Hello everyone, in this problem we need to find the absolute minimum and the absolute maximum values for the given functions over the interval.
00:10
So, the first function we are given as f of x to be equal to absolute value of 6 minus 4x on the interval minus 3 to 3.
00:23
So, first in order to find the absolute maximum and the minimum values, first we need to find the critical point for this.
00:30
So, for that we need to find the derivative for the given function.
00:33
So, first f dash of x will be equal to d by dx of absolute value of 6 minus 4x.
00:42
So, now, taking differentiation we have this value to be 4x minus 6 divided by absolute value of 4x minus 6 multiplied by d by dx of 4x minus 6.
01:00
So, now differentiating this with respect to x we have this value to be 4x minus 6 multiplied by 4 divided by absolute value of 4x minus 6.
01:15
So, multiplying this we have this value to be 16x minus 24 divided by absolute value of 4x minus 6.
01:24
So, this is the first derivative.
01:27
So, now we need to equate the first derivative to 0 in order to obtain the critical points.
01:36
So, now equating the first derivative which is of 16x minus 24 divided by absolute value of 4x minus 6 to be equal to 0 we have the value of 16x minus 24 to be equal to 0.
01:53
So, from this we get the value of x to be equal to 3 by.
01:59
So, now we have the value of x.
02:03
So, this is the critical point.
02:12
So, now over the interval here it is of minus 3 to 3.
02:16
So, at x equal to minus 3 we can have the given function f of x as 14 sorry 6 absolute value of 6 minus 4x.
02:30
Now substituting the value of x to be minus 3 here...