On what intervals is the graph of f(x)=x^3-2x^2+5x+1 increasing?

on what intervals is the graph of f(x)=0.5x^2-6 decreasing?

on what intervals is the graph of f(x)= increasing?

the graph of the parabola is above the x-axis, so the derivative is always positive and therefore the initial function is increasing in its whole domain.


The function is decreasing when its first derivative is negative. The first derivative of this function is negative for so for the function is decreasing.


The function is increasing when its first derivative is positive. The first derivative of this function is always negative therefore this function is never increasing.