Answer using the f(x)

Question

f(x)=7x/(x^2-25)

f) use interval notation to indicate where f(x) is concave up

g) use the interval notation to indicate where f(x) is concave down

Answer 1

f'(x) = 7(x²- 25 - 2x²)/(x² - 25)² = -7(x² + 25)/(x² - 25)²; f'(x) = - 7[2x(x² - 25) - 4x(x² + 25)]/(x² - 25)³ =

7(2x³ + 150x)/(x² - 25)³; f''(x) = 0; x = 0

f) f''(x) > 0, (- 5, 0), (5, ∞) f(x) concave up

g)f''(x) < 0; (- ∞, - 5), (0, 5) f(x) concave down