00:01
Hello students, this is a graph of f of x.
00:04
Okay, so we have to find out for what values of x is the second derivative is positive.
00:10
And we'll be having four options.
00:12
Option a, f double dash or f prime, double prime is always positive.
00:18
F double prime is never positive and minus 2 less than pi less than 2 and minus infinity less than pi less than 0.
00:25
So we have to find out which is the correct option.
00:28
Before we move on to the solution, we can first look what is a second derivative, what is an f of.
00:35
Let's consider an example.
00:38
Let f of x will be equal to negative 5 x squared.
00:47
So first derivative, it means that differentiate this function with respect to x.
00:54
So here it will be minus 5, x squared, it will be 2x.
00:59
So that will be equal to negative 10x.
01:03
Now, second derivative, it means that differentiate this again with respect to x.
01:09
So here it will be negative 10.
01:12
Okay, so this is how we calculate the derivative.
01:15
Okay.
01:16
Now, for the given figure, we have let f of x be a function.
01:25
Okay, for this function, we can have either slope, increases either slope increases or either slope decreases, or either slope decreases, okay? either slope decreases.
01:50
For concave upward, concave upward, they have the slope increases...
