00:01
First, we are given a function f of x equal to x cubed by 5 plus 3x square.
00:06
So the first derivative of this function is given by this expression.
00:11
The second derivative is given by this expression.
00:15
A point of inflection is where the first derivative, which is f prime, and the second derivative, which is f double prime, both of them vanish.
00:27
Now, f prime is equal to 0, is given by this.
00:31
Four solutions if double prime equal to zero is given by these three solutions and the common solution is at x equal to zero so x equal to zero is the point of inflection in fact if we plot if of x against x as in this curve the from the curve we can clearly see that the origin is the point of inflection for this curve next we are given a second function which is equal to 5x plus 7 by x now quickly we can draw the function itself, its first derivative f prime and its second derivative f double prime.
01:09
Now a and c at the critical values, that means a and c are the points where the first derivative vanishes.
01:18
That means 5 equal to 7 by x square or x equal to plus minus square root of 7.
01:31
By 5.
01:39
Now b is the point where fx actually is undefined in fact we see that for x equal to zero the function blows up so so as x tends to zero mod of f tends to infinity so it goes to plus infinity or minus infinity depending on the sign of x so a is the point minus of square root of 7 by 5.
02:19
C is the point plus square root of 7 by 5.
02:23
B is the point 0.
02:25
So here we can mark this point.
02:27
So this is the point a...