f(x)=12ln(x)−x2+5x>0f(x) = 12\ln(x) - x^2 + 5 \quad x > 0f(x)=12ln(x)−x2+5x>0
Show that y=f(x)y = f(x)y=f(x) has a stationary point in the interval [2.4,2.5][2.4, 2.5][2.4,2.5]
Starting with x0=2.45x_0 = 2.45x0=2.45, apply the Newton-Raphson procedure twice to find an approximation for the x x\,x coordinate of the stationary point in the interval [2.4,2.5][2.4, 2.5][2.4,2.5]. Give your answer to 3 decimal places.