Differentiation - Connected Rates of Change

IB AA SL: core and optional content

Core: monotonicity and stationary points. Optional: the final connected rate with respect to time.

A function is defined by the equation \(y=4x^2-x^3+11x-30\).

1. Find the range of values of \(x\) for which \(y=4x^2-x^3+11x-30\) is an increasing function.
2. Find the \(x\)-coordinate of the stationary points of the curve and determine the nature of each stationary point.
   
   
3. The rate of change of \(x\) is \(0.05\) units per second when \(x=1\). Find the corresponding rate of change of \(y\).