1) Give an example of a function that has a local maximum at x = 1 and x=3 and a local minimum at x = 2 2) Find the intervals of increase and decrease of your function in part (1)

Question

1) Give an example of a function that has a local maximum at x = 1 and x=3 and a local minimum at x = 2

2) Find the intervals of increase and decrease of your function in part (1)

Answer 1

f'(x) = y = -(x-1)(x-3)(x-2) = -(x^2-4x+3)(x-2)

f'(x)= -x^3+5x^2-11x+6

integrate to get the function

f(x)= -x^4/4 +5x^3/3 -11x^2/2 +6x + any constant. It's graphically "M" shaped

y= (-1/4)x^4 +(5/3)x^3 - (11/2)x^2 +6x + 46

is an example of a function with two local maximums at x=1 and 3, and one local minimum at x=2

intervals of increase are (1,2)U(3, infinity)

interval of decrease is (2,3)