Him what would the derivative graph of this look like? ...

Question

firekat97 · Answer

attachment

firekat97 · Answer

Hi* whoops

beginnersmind · Answer

Split it up into intervals where the function can be represented with a single formula.

e.g for x in [0,1[, f(x) = 3
for x in [1,5[ , f(x) = (3/2)*(x-1) + 3

and so on.

You can calculate the derivatives for these pieces easily. Remember that at points like 1,5 or 7 the derivative doesn't exist.

beginnersmind · Answer

correction:
for x in [1,5[ , f(x) = -(3/2)*(x-1) + 3

firekat97 · Answer

ohh okay thanks! And I'm guessing we do a similar thing if we're working backward? So, finding the integral graph instead?

beginnersmind · Answer

I think I would just use the area definition of the integral, especially for a simple function like this.

BTW, we could have solved this by remembering that the derivative of a linear function is its slope and just 'reading off' the value from the graph.

firekat97 · Answer

Okay I think I get it, thanks :)

beginnersmind · Answer

No problem :)