00:02
In this problem, we are given the function g of x is equal to x cube minus 2x square minus 4x minus 3 and we are asked to determine the relative extreme points of this function and thereby graph the function.
00:17
Now the relative extreme points are the points of the function where the first derivative of the function which is g dash of x is equal to 0.
00:27
And this x values corresponds to the critical points of the function and the function value at the critical points are the extreme values.
00:35
So first find the points where the first derivative is equal to zero.
00:40
Determine the first derivative of this function, it is 3x square minus 4x minus 4 and equate it to 0 to solve for x.
00:48
This equation can be solved by fact rising.
00:52
So split the middle term as 3x square minus 6x plus 2x minus 2x minus 2x minus 4x.
00:57
Minus 4 is equal to 0.
00:59
From this we get 3x times x minus 2 plus 2 times x minus 2 is equal to 0.
01:07
That is 3x plus 2 times x minus 2 is equal to 0...