??? - 2013 JUNE Q4
4. f(x) = 25x2e2x
– 16
(a) Using calculus, find the exact coordinates of the turning points on the curve with equation y = f(x). (5)
(b) Show that the equation f(x) = 0 can be written as x = ±4/5e–x (1)
The equation f(x) = 0 has a root a, where a = 0.5 to 1 decimal place.
(c) Starting with x0 = 0.5, use the iteration formula xn+1 = ±4/5e–x to calculate the values of x1 , x2 and x3, giving your answers to 3 decimal places. (3)
(d) Give an accurate estimate for a to 2 decimal places, and justify your answer. (2)
(a) Using calculus, find the exact coordinates of the turning points on the curve with equation y = f(x). (5)
(b) Show that the equation f(x) = 0 can be written as x = ±4/5e–x (1)
The equation f(x) = 0 has a root a, where a = 0.5 to 1 decimal place.
(c) Starting with x0 = 0.5, use the iteration formula xn+1 = ±4/5e–x to calculate the values of x1 , x2 and x3, giving your answers to 3 decimal places. (3)
(d) Give an accurate estimate for a to 2 decimal places, and justify your answer. (2)