Skip to main content
Back

Basic Graphing of the Derivative definitions

Control buttons has been changed to "navigation" mode.
1/15
  • Derivative
    Numerical value representing the slope of a tangent line to a function at a specific point.
  • Tangent Line
    Straight line that just touches a curve at a point, matching the curve's instantaneous direction.
  • Slope
    Measure of steepness or incline of a line, indicating how much the function rises or falls.
  • Interval
    Continuous range of x-values over which a function's behavior is analyzed for changes in slope.
  • Peak
    Highest point on a graph where the tangent line is flat and the derivative equals zero.
  • Valley
    Lowest point on a graph where the tangent line is flat and the derivative equals zero.
  • Discontinuity
    Point on a graph where the function jumps or breaks, causing the derivative to not exist.
  • Sharp Corner
    Point where the graph changes direction abruptly, resulting in an undefined derivative.
  • Constant Function
    Graph segment where the output remains unchanged, leading to a zero derivative throughout.
  • Zero Slope
    Situation where the tangent line is horizontal, indicating no increase or decrease in the function.
  • Positive Slope
    Condition where the tangent line rises as x increases, showing the function is increasing.
  • Negative Slope
    Condition where the tangent line falls as x increases, showing the function is decreasing.
  • X Axis
    Horizontal reference line on a graph where a zero derivative is represented.
  • Jump
    Sudden change in the graph's value, often leading to a non-existent derivative at that point.
  • Output
    Value produced by a function for a given input, visualized as the y-coordinate on a graph.