Functions of Graphs

Question

Let f(x) = ax + b/x. What are the critical points of f(x)?

Answer 1

Functions of Graphs

Let f(x) = ax + b/x. What are the critical points of f(x)?

f(x) = ax + b/x = ax + bx^-1

f ' (x) = a – bx^-2 = a – b/x²

For critical points: f ' (x) = 0 ==> a – b/x² = 0 ==> a = b/x² ==> x² = b/a ==> x = ±√(b/a)

y = f(±√(b/a)) = a(±√(b/a)) + b/(±√(b/a)) = ±(a)√(b/a)) + ±(b)/√(b/a)) = ±√(ab) + ±√(ab) = ±2√(ab)

(x, y) = (±√(b/a), ±2√(ab))