Apply Newton's Method to f (x) = 4x4 - 6x2 - 11/4 with starting guess x0 = 1/2. find the approximate root.

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

Find شان y=√x

Find f. = 6 + 6x + 36x², f(0) = 3, f(1) f(1) = 14 f"(x) =

Water is leaking from a tap at a rate of x cm³/min. (a) Write down an expression for the time taken to collect 50 cm³ of water. (b) When the tap is tightened, the water leaks at 3 cm/min less. Write down an expression for the time taken to collect the same amount of water. (c) The difference between the two times is 1.5 minutes. Form an equation in x and show that it reduces to x-3x-100 = 0. (d) Solve this equation, giving your answers correct to 1 decimal place. (e) Hence, find the time taken to collect 50 cm of water, correct to the nearest second, before the tap is tightened.

x) = (1/3)x - 6