Question 40
The diagram shows a sketch of the curve C C\,C with equation y=2x32−5x+ex+4\displaystyle y = 2x^{\frac{3}{2}} - 5\sqrt{x} + e^x + 4y=2x23−5x+ex+4
a.[3]
Show that dydx=3x+ex−52x\displaystyle \frac{dy}{dx} = 3\sqrt{x} + e^x - \frac{5}{2\sqrt{x}}dxdy=3x+ex−2x5
b.[2]
The point P P\,P is the minimum turning point on CCC. Show that the x x\,x coordinate of P P\,P is a solution of
x=5−2xex6 x = \frac{5 - 2\sqrt{x}e^x}{6} x=65−2xexc.[3]
Use the iteration formula xn+1=5−2xnexn6\displaystyle x_{n+1} = \frac{5 - 2\sqrt{x_n}e^{x_n}}{6}xn+1=65−2xnexn with x1=0.5x_1 = 0.5x1=0.5 to find (i) the value of x2 x_2\,x2 to 5 decimal places, (ii) the x x\,x coordinate of P P\,P to 5 decimal places.
Numerical Methods Questions
80 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.