Question

Use the first derivative to determine where the function f(x)=5x^4+1280x is increasing and decreasing

Answer 1

f(x) = 5x^4 + 1280x
f'(x) = 20x^3 + 1280

f'(x) = 0 = 20x^3 + 1280
-1280 = 20x^3
-64 = x^3
x = -4

Answer 2

This value is a critical point, so you just need to test on either side of this x-value to determine increasing (positive value) and decreasing (negative value) parts of the interval.