Question

also interval on which f is concave down

Consider the equation below. (If an answer does not f(x) = x2 - 6x2 - 15x + 6 (a) Find the interval on which f is increasing. (-∞, -1), (5,00) Find the interval on which f is decreasing. ( (-1,5) (b) Find the local minimum and maximum local minimum value -94 local maximum value 14 (c) Find the inflection point. (x, y) = Find the interval on which f is concave up

Answer 1

Q- f(x) = x3_6x²_15x + 6 f'(x) = 3x²-12% -15 3(2-5)(x+1) f'(x) 6x -12 61 x - 2) Sign of f'(x) + og Sign of flo 2 a) for increasing - f(x) > 0 - < < (- 0,-1) 0 (s, for decreasing - f (xico > < < (-1,5 )

b). Critical point - f'(X) = 0 3 312-5) (2+1) = 0 x = -1,5 Sign of f* (*) at x = -1 3) f"(-1) = 6(-1-2) -ve at x = -1 > local Max. Local Max _ f(-1) (-103-6(-112_15(-1) +6 = iu Aus Sign of f"(*) at x= 5 f" (5) = 6(5-2) the 1 at 2=5 local Min fle 5) = 53-6x5 x52 -15x5 +6 -94 . Aus

c) - Inflection point f (x) =0 = 6(x-2) 3 x=2 y = $12) = 23-6x2²-15x2+6 -40 (ay) (2,-40) d) for Concque up - of'(x) >o 3 x G (2, 0) for Concame down f" (also =) 26 (-00, 2 Ang 1