Calculus, where tangent line is horizontal

Question

Find the point(s) on the graph of f where the tangent line is horizontal. (If an answer does not exist, enter DNE.)

 

f(x) = (x)/ (x^2 + 4)

Answer 1

f'(x) must be zero at those points.

f'(x) = [(x² + 4) - x(2x)] / (x² + 4)² = 0

-x² + 4 = 0

x² = 4

x = ±2

Evaluate f(x) at these 2 values of x to get the y-coordinates. You can finish from here.