How do I prove that functions increase? (1 Viewer)

[jks22]

f(x) = -3/x, so f'(x) = 3/x^2 but how do I prove that it increases within its domain?

 

[Lith_30]

Since the derivative is for all real x, since square numbers are positive and .

Therefore for all values of x within the domain of would be increasing.

 

[jks22]

Since the derivative is for all real x, since square numbers are positive and .

Therefore for all values of x within the domain of would be increasing.

Thanks appreciate it! So if I prove it's always positive, can I say that a function is always increasing?

 

[5uckerberg]

Thanks appreciate it! So if I prove it's always positive, can I say that a function is always increasing?

Yes because once you have found the minimum turning point the function will only increase from the minimum turning point. If there is something lower than the minimum turning point you need to go back and check your calculations because there might be something lower.

 

[Lith_30]

Yes because once you have found the minimum turning point the function will only increase from the minimum turning point. If there is something lower than the minimum turning point you need to go back and check your calculations because there might be something lower.

But for this specific question there is no minimum turning point, cause .

 

[5uckerberg]

Well, since then the function is always increasing. Since you are doing Mathematics Advanced this concept will be a very useful one in the topic that many HSC candidates struggle with Cumulative Density Function found in the last chapter. Keep this question in your back pocket it may come in handy.