Move the blue point on the `x`-axis to change the value of `c`, and observe how the line tangent to the `f`-graph at `x = c` changes. When is the slope of the tangent line greatest? lowest? Can you find (at least) one value for `c` where the tangent line crosses the `f`-graph only once, at its point of tangency? Improve your math knowledge with free questions in "Relations: convert between tables, graphs, mappings and lists of points" and thousands of other math skills.
Graph showing the relationship between the roots, turning or stationary points and inflection point of a cubic polynomial and its first and second derivatives by CMG Lee. The vertical scale is compressed 1:50 relative to the horizontal scale for ease of viewing.