find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.

Question

f(x)= x³+4x—5

Answer 1

f(x) = x³ + 4x - 5

 

f'(x) = 3x² + 4

 

f'(x) > 0 for all x

 

So, f is increasing on (-∞, ∞)

      f is never decreasing

 

Since the function is differentiable for all x and the derivative does not change sign, there are no relative extrema.