Find all intervals on which \(f\) is concave up and those on which \(f\) is concave down. Find the \((x,y)\) coordinates of all inflection points, if any. Sketch the graph of \(y=f(x)\) using all of ...

is decreasing. If \(f\) is a polynomial function, what is the least possible degree of \(f\text{?}\) Figure 3.2.2. The graph of \(\ds f^\prime(x)\) Sketch the graph of \(f(x)=3x^4-8x^3+10\text{,}\) ...

Sketch \(y = x^2 - 6x + 4\). The coefficient of \(x^2\) is positive, so the graph will be a positive U-shaped curve. Writing \(y = x^2 - 6x + 4\) in completed square form gives \(y = (x - 3)^2 - 5\).