1. The big idea
Read a graph left to right. If it climbs, the function is increasing; if it falls, decreasing; if it stays level, constant. For xā < xā in an interval:
Increasing: f(xā) < f(xā) | Decreasing: f(xā) > f(xā) | Constant: f(xā) = f(xā)
Slope > 0
fā²(x) > 0 ā increasing ā
fā²(x) > 0 ā increasing ā
Slope < 0
fā²(x) < 0 ā decreasing ā
fā²(x) < 0 ā decreasing ā
Slope = 0
fā²(x) = 0 ā constant ā
fā²(x) = 0 ā constant ā
š Link to derivatives: fā²(x) is the slope of the tangent line. So the sign of fā² tells the direction of the graph. Where fā² changes sign, the graph turns around (a local max or min).
2. Explore famous functions
Pick a function, then drag the slider. The tangent line shows the slope; the graph is coloured š¢ increasing, š“ decreasing, āŖ constant. The coloured strip under the x-axis is the interval map.
3. šÆ Practice quiz (24 MCQs)
šŗ Learn more
šŗ To learn any topic in detail, watch our free lectures and read the notes on our website mformathodology.com and on our YouTube channel @MforMATHODOLOGY.
Instructor: Rabbia Abid Khan Ā· MforMathodology