A function is increasing on a particular interval if for any, then Ie: As x increases, A function is decreasing on a particular interval if for any, then Ie: As x increases, For a continuous and differentiable function, f(x), the y-values are increasing for all x-values when and the y-values are decreasing for all x-values when Eg.1: Find the intervals of increase and decrease for the function, f (x) = 2x3 - 3x2 -12x Interval Value of f '(x) Slope of Tangent Y-values are Eg.2: Find the intervals of increase and decrease for the function, f (x) = x- 3x3 Interval Value of f '(x) Slope of Tangent Y-values are\""' "O 0 Discontinuity Eg.l: Determine the critical points for y = x3 6x2. Sketch the graph. Solution: _ will be a local maximum and will be a local minimum. Eg.2: Determine the critical points for y = x4 8x3 + 18x2 and state whether these values gives a local maximum, 21 local minimum or neither for the function. Solution