Question

Many diabetics need to control their blood sugar levels with insulin. Below is a graph that shows blood sugar levels over time after insulin is given to a "normal person" at time, t = 15 minutes. As you can see insulin causes blood sugar levels to drop. Where is the function not differentiable and why?
A. The function is differentiable everywhere.
B. The function is differentiable everywhere except t = 30.
C. The function is differentiable everywhere except t = 15, t = 30, and t = 40 where there are corners.
D. The function is differentiable everywhere except at t = 15 where there is a

Answer 1

you know the exaxct meaning of "differentiable"?

Answer 2

yes

Answer 3

can you tell me?

Answer 4

its a function whos derivative exists over its entire domain

Answer 5

more or less. Better would say that a function can be aproximated by a linear function at any point of it's domain.
Linear function is a function of a type f(x)=kx+b, where k is some constant.
To be able to find this linear function we need it actualy to have a derivative. It can be shown, that this constant k that I mentioned befor, is actulay a value of the derivative at the point in question. Ok for now?

Answer 6

yea

Answer 7

Imagine a non linear function:

Answer 8

It can be aproximated at a point with a liner function: