25.11.25.md (539B)
1 25/11/25 2 ======== 3 4 - to sketch a curve 5 - you need to find the derivative 6 - then find the critical points (when f'(x) = 0) 7 - sub in the critical points and the start and end points to the original function 8 - use these to sketch the graph 9 - on a concave curve f'(x) will get larger as x rises, or smaller if the curve is in the other way 10 - f''(x) > 0 for all values on x on the curve is the graph is concave upward 11 - f''(x) < 0 for all values on x on the curve is the graph is concave downward 12 - it will be 0 for points of inflection