Increasing Intervals - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 3.3 Notes Learning Targets... 1. Determine increasing/decreasing intervals of a function 2. Use Ist Derivative Test find relative extrema LT: Determine increasing/decreasing intervals of a function ® Graphically... o “Increasing”: where “Slope” is positive o “Decreasing”: where “slope” is negative e = Analytically... © “Increasing”: where 1" derivative is positive ° “Decreasing”: where 1 derivative is negative o Do you see the connection? @ These will always be open intervals (at endpoints, the “slope” is zero) Find the increasing/decreasing open intervals graphically & analytically. \ + (290 ,- 1) f(x) = 2x4 + 16x? Sea: Gee,-T) (6,2) E'Cx) s- 48 +3r% =O 6 ~ -¢xG-) CRAT &'S! XK = - 230, (=605-2) CCB) =o 0 = her, (2,0) (Ay = -2y <0 + DELR. (eo, EU) = v4 0 6 ive. DER: (-2,0)(2, 9) (2 bo) ECs) = -1 20 608 DEER Identify the open intervals on which the function is increasing or decreasing. 2 4 -! yards =x+4x ight Ey i Ke-4 | Cee OED) =O x x* ea x* =0 CRAT te $2 ye —B9O5% (-08,-) B(-»=%>0 \sen. (- 220) £'C1D 2-340 DECK: (ot) FCI) =-3<6 “ Ga Foie 1/2