Determining Monotonicity Using First Derivative
Consider the function \(f(x) = x^3 – 3x + 2\). Determine the intervals where the function is increasing and decreasing by finding the sign of its derivative.
Analysis of Polynomial Turning Points
Consider the polynomial function \(f(x)= x^4 – 4x^2 + 1\). Sketch its graph, clearly marking the turning points and points of inflection. Determine the coordinates of the turning points and state the intervals on which \(f(x)\) is increasing and decreasing.