INTRODUCTION TO A CUBIC FUNCTION

By molefiphenyo6 | Updated: Sept. 24, 2022, 8:46 a.m.

Slideshow Video

SHARE THE AWESOMENESS

Education

create your own animated videos for free

_abc cc

* Powtoon is not liable for any 3rd party content used. It is the responsibility of each user to comply with 3rd party copyright laws.

Embed code

Select a size, the embed code changes based on your selection.

_abc Powtoon Transcript

CUBIC FUNCTION
MATHEMATICS 
GRADE 12
BY MR MOLEFI
A cubic function is a polynomial function of degree 3 and is of the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are real numbers and a ≠ 0
What is a cubic function?
f(x) = ax^3 + bx^2 + cx + d, is a general equation of cubic function
 a ≠ 0, because Ais a leading term and it gives you a shape of your graph.
in the equation, D IS Y-INTERCEPT
this will give you an image of cubic function
NOW, THINK ABOUT THIS
Add Text
If the linear function have no turning point and quadratic have only one turning point, so, how many turning point are in the cubic function
now, this is how the cubic function looks like:
and it has 2 turning point and 1 point of inflection
POINT OF INFLECTION
TURNING POINT
SINCE I SAID A IN THE GENERAL EQUATION SHOWS THE SHAPE OF THE GRAPH, LET ME SHOW YOU HOW: 
A>0
THIS MEANS THAT THE GRAPH WILL START BY INCREASING WHEN THE (A) IS GREATER THAN 0, WHICH MEANS THAT (A) IS A POSITIVE NUMBER
AGAIN, WHEN THE CUBIC FUNCTION STARTS BY DECREASING, WHICH MEANS THAT (A<0)
THIS IS HOW THE CUBIC GRAPH LOOKS LIKE WHEN (A) IS NEGATIVE
now let's talk about the turning points of cubic function 
First, we use first derivative to find the x value of turning points in the cubic function.
secondly, the equation of first derivative  of cubic function is F(X)'=3ax^{2}+2bx+c.
Thirdly, I hope that you have noticed that the first derivative of cubic function is a quadratic function. Further the first derivative looks like this in a sketch:
PLEASE NOTE THAT: The x value of turning points in the cubic function are equals to x-intercept in a quadratic equation and point of inflection in the cubic function is equals to x value of a turning point in a quadratic equation.
Therefore, to get x-values of the turning points in cubic function, you have to substitute f(x) as 0 in a first derivative. You want to know why?
This is because you have to find the x intercepts of quadratic function as they are equals to x value of turning points in cubic function. and when you find x-intercepts always F(x)=0. After getting those x-values, you have to substite them on your general equation of cubic function to get y value of a turning point.
Now, let's talk about point of inflection:
Firstly, the point of inflection is a second derivative of cubic function
Secondly, the equation of second derivative is F(x)=6ax+2b 
Remembering: point of inflection is equals to the turning point of first derivative of cubic function.
Thirdly, i hope you have noticed that the equation of point of inflection is a linear equation.
lastly, in the same equation of second derivative, the x value of x-intercept is a point of inflection and which means that is a x-value of turning point in first derivative graph.
Now, check the picture of second derivative and first derivative:
cubic function
second derivative
First derivative
To find point of inflection, you must substitute F(x) as 0 because you have to find the x value of x-intercept of second derivative to get point of inflection and x value of the turning point of quadratic function.
the examples and x-intercepts will be introduced in the next video
additional information: this video presents the introduction of a cubic function and please take notes when watching this video.
THANK YOU FOR WATCHING MY VIDEO
PLEASE LIKE THE VIDEO

INTRODUCTION TO A CUBIC FUNCTION

Copy this link to share with friends and colleagues:

WELCOME TO POWTOON!