Find the x-coordinate of the point(s) of inflection on the graph of y = x^3 - 12x^2 - 5.

y"=6x-24 = 6(x-4)

you want y"=0

To find the x-coordinate of the point(s) of inflection on the graph, we need to find the second derivative of the given function and then solve for x when the second derivative equals zero.

Step 1: Find the first derivative of the function.
The first derivative of y = x^3 - 12x^2 - 5 is given by:
dy/dx = 3x^2 - 24x

Step 2: Find the second derivative of the function.
To find the second derivative, we differentiate the first derivative with respect to x again.
d^2y/dx^2 = d/dx(3x^2 - 24x)
= 6x - 24

Step 3: Set the second derivative equal to zero and solve for x.
6x - 24 = 0
Simplifying the equation, we get:
6x = 24
Dividing both sides by 6, we find:
x = 4

Therefore, the x-coordinate of the point of inflection on the graph of y = x^3 - 12x^2 - 5 is x = 4.

To find the x-coordinate(s) of the point(s) of inflection on the graph of the function y = x^3 - 12x^2 - 5, we need to follow a few steps:

Step 1: Find the second derivative of the function.
The point(s) of inflection occur where the concavity of the graph changes. So, we need to find the second derivative to determine the concavity of the function.

y = x^3 - 12x^2 - 5

Taking the derivative twice, we get:

y'' = d^2/dx^2 (x^3 - 12x^2 - 5)
= 6x - 24

Step 2: Set the second derivative equal to zero and solve for x.
To find the x-coordinate(s) of the inflection point(s), we set the second derivative equal to zero and solve for x:

6x - 24 = 0

Adding 24 to both sides:

6x = 24

Dividing both sides by 6:

x = 4

Step 3: Determine the x-coordinate(s) of the point(s) of inflection.
The x-coordinate(s) of the inflection point(s) is/are given by the solution(s) to the equation found in Step 2. In this case, we found x = 4.

Therefore, the x-coordinate(s) of the point(s) of inflection on the graph of y = x^3 - 12x^2 - 5 is x = 4.