Blog #4

Asma  Aljarbou

Math-211 

Blog #4

Hello my students my name is Professor Asma 

Today I am going to teach you the Derivative of Constant !!

My mission today is to explain what is the derivative of constant is, how to find it and how it could be useful in real life for us.

Math is fun and surround us everywhere we go  

Definition:

Constant function is F (x) = K, where “K” can be any number.

For that the derivative of constant function is zero because for any constant function the slope of that line always constant which equal to zero. The slope = rise/ run, and in the graph below the slope of the horizontal line in the middle equal zero. For example, if assume that Y = 5 that’s means Y = 0x + 5 then the slope = 5 and if we pick two points (2 , 5) (4 , 5) à slope = y2-y1/x2-x1 = 5 -5/4 -2 = 0/2 =0

 For that the derivative of constant = 0. It is that simple 

                                                                                           

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Formula:

If F(x) = C Then F’(x) = 0

And to show you proof that the derivative of constant is always = 0

If we assume that F(x) = C then by taking the derivative of F’(x) using the limit of the function

Thus:

F’(x) = Lim F (x + h) – F (x) / h = Lim C - C/ h = Lim 0/h = 0

             hà0                                                       hà0                            hà0

If you think that 0/h is not zero because we have zero denominator well that’s not totally right.

0 < | h |, where h cannot be equal to 0 for that |0/h | = 0.

Working Examples:

Find the derivative of F(x) = -3.67?

F’(x) = 0 or it can be written as d/dx = 0

Find the derivative of F(x) = 1/38 ?

F'(x) = 0

Real use:

*If want to think of a real example of the Derivative of a constant function well think of if deposit an amount of money in the bank that has no any interest rate so the money you deposits will be the same no matter how ing it stay at your bank account.

*One more example would be if we think of the ship speed at certain time they speed will be constant and does not change.

Helpful links that show you how to calculate the constant derivative and gave you some good examples !!

https://www.youtube.com/watch?v=PwWwyxGBw_8

https://www.youtube.com/watch?v=YdxeLS2qvp4

https://www.mathsisfun.com/calculus/derivatives-rules.html

I hope you learn it well because next week we will have small quiz over what we go through Today make sure to go over it one more time before the next class

Have good day