f(x)=12x2+5cos(x)\displaystyle f(x) = \frac{1}{2}x^2 + 5\cos(x)f(x)=21x2+5cos(x)
Show that y=f(x)y = f(x)y=f(x) has a stationary point in the interval [2.5,2.6][2.5, 2.6][2.5,2.6]
Starting with x0=2.55x_0 = 2.55x0=2.55, apply the Newton-Raphson procedure twice to find an approximation for the x x\,x coordinate of the stationary point in the interval [2.5,2.6][2.5, 2.6][2.5,2.6]. Give your answer to 3 decimal places.
