larger x-value (x, y). smaller x-value (x, y)

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+9

Answer 1

f'(x) = (1·(x² + 9) - 2x·x)/(x² + 9)² = (9 - x²)(x² + 9)² = 0; 9 - x² = 0; x = ±3;

x = 3 y = 3/18 = 1/6; (3, 1/6);

x = - 3, y = -3/18 = - 1/6; (- 3, 1/6)^