Question

F(x)=x^3+5/2x^2-28x Find critical numbers

Answer 1

Answer:

x = 0.761, 2, 14

Step-by-step explanation:

critical numbers are points where f'(x) = 0 or undefined and the endpoints

since there are no endpoints for the domain, we just consider the points where f'(x) is 0 or undefined

$\frac{d}{dx}$ $(\frac{x^3+5}{2x^2-28x})$ = $\frac{(3x^2+5)(2x^2-28x)-(4x-28)(x^3+5)}{(2x^2-28x)^2}$

undefined at (2x²-28x)², 2x² -28x=0

2x(x-14) = 0

x = 2,14

0 at (3x²+5)(2x²-28x)-(4x-28)(x³+5)

x = 0.761