Question

Ella thinks that if a function is positive over an interval, then its derivative is also positive. Is Ella correct? Explain.

Thank you!!

Answer 1

If a function is positive that simply means that its graph lies above the
x-axis.
However, it could be decreasing, thus its derivative would be negative for that domain.
e.g. y = -x^2 + 9
from x = 0 to x = 3, the function is positive,
but dy/dx = -2x would be negative for those same x values.

So Ella is incorrect.