Question

if i am given the graph of a derivative, how do i determine where the orginal function is increasing or deacrasing???

Answer 1

Whenever the graph of the derivative is above the x-axis, the original function is increasing. Conversely, when it is below the x-axis, it is decreasing.

This is because the derivative is the slope of the tangent line. Positive slope means increasing, negative slope means decreasing.