f(x)=3xex−1f(x) = 3xe^x - 1f(x)=3xex−1. The curve with equation y=f(x)y = f(x)y=f(x) has a turning point PPP.
Find the exact coordinates of PPP.
The equation f(x)=0f(x) = 0f(x)=0 has a root between x=0.25x = 0.25x=0.25 and x=0.3x = 0.3x=0.3. Use the iterative formula
xn+1=13e−xn x_{n+1} = \frac{1}{3}e^{-x_n} xn+1=31e−xnwith x0=0.25x_0 = 0.25x0=0.25 to find, to 4 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
By choosing a suitable interval, show that a root of f(x)=0f(x) = 0f(x)=0 is x=0.2576x = 0.2576x=0.2576 correct to 4 decimal places.
Practise Edexcel A Level Old Maths Numerical Methods with exam-style questions for A Level Old Maths. 7 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.