Why have these endpoints been excluded?

[Darkmisc]

Homework Statement

The problem asks for the derivative of a piecewise function. I don't know why it has excluded the endpoints from the correct answer.

Relevant Equations

f(h) = 4h+10 0<=h<=9/4
f(h) = 0.5sin[2pi/5(h-9/4)]+19 9/4<h<=24

Hi everyone

Could someone please confirm that these solutions are correct? They exclude the endpoints 0 and 24, but I don't understand why, since f(h) includes 0 and 24.

I understand why 9/4 is excluded, as the derivative is not a continuous function.

Thanks

 

[PeroK]

Homework Statement:: The problem asks for the derivative of a piecewise function. I don't know why it has excluded the endpoints from the correct answer.

Generally the derivative of a function $f$ at the point $a$ requires the function to be defined in some neighbourhood of $a$ (i.e. open interval containing $a$). That said, it's not very important in this case whether we consider $f'$ to be defined at $0$ and $24$ or not.

I understand why 9/4 is excluded, as the derivative is not a continuous function.

Technically the derivative is not defined for $h = \frac 9 4$.

 

[Prof B]

That said, it's not very important in this case whether we consider $f'$ to be defined at $0$ and $24$ or not.

The minimum and maximum of a function occur where its derivative is 0 or undefined.