Consider the function f(x) = 5/4x^4 + 2/3x^3 - 5x^2 - 4x + 5

Question

a. Find any relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values.

b. Determine the interval(s) where f(x) is increasing (if any) and the interval(s) where f(x) is decreasing (if any).

c. Determine the number of inflection points for this function and find their x-coordinate(s).

d. Determine whether f(x) is concave up or down at the following points: x = -2, x = -1, x = 0, and x = 2. Use this information and the information in parts A - C to sketch this function.

I really need help, and any help is greatly appreciated.

Answer 1

y = 5/4x^4 + 2/3x^3 - 5x^2 - 4x + 5
y' = 5x^3 + 2x^2 - 10x - 4 = (5x+2)(x^2-2)
y" = 15x^2 + 4x - 10

a. extrema where y'=-
max if y" < 0, min if y" > 0

b. increasing where y' > 0

c. inflection points where y" = 0

d. concave up if y" > 0

Now just plug in your numbers and functions.

Answer 2

To check:
https://www.wolframalpha.com/input/?i=%285%2F4%29x%5E4+%2B+%282%2F3%29x%5E3+-+5x%5E2+-+4x+%2B+5