Plug in any remaining info and solve Air is being pumped into a spherical balloon at 10 cm3/min. Calculate the rate at which the radius of the balloon is increasing when the diameter is 15 cm. Triangle ABC is right angled at A, and AB = 20 cm. <ABC increases at a constant rate of 1˚ per minute. At what rate is BC changing at the instant when <ABC measures 30˚? Two wizards Arthur and Beatrix leave Harry Potter’s house at 130˚ to one another, with constant speeds of 12 m/s and 16 m s-1 respectively. Find the rate at which the distance between them is changing after 2 minutes. Knowledge Check-in The function is defined by (x) = e2x. It can be shown that (x) = (2n + 2n−1) e2x for all where (x) f f x f x n n+, f (n) (n) represents the derivative of (x). nth f (a) By considering (x) for =1 and = 2, show that there is one minimum point P on the graph of and find f n n f, (n) the coordinates of P. (7) (b) Show that has a point of inflexion Q at = f x −1. (5)
Plug in any remaining info and solve Air is being pumped into a spherical balloon at 10 cm3/min. Calculate the rate at which the radius of the balloon is increasing when the diameter is 15 cm. Triangle ABC is right angled at A, and AB = 20 cm. <ABC increases at a constant rate of 1˚ per minute. At what rate is BC changing at the instant when <ABC measures 30˚? Two wizards Arthur and Beatrix leave Harry Potter’s house at 130˚ to one another, with constant speeds of 12 m/s and 16 m s-1 respectively. Find the rate at which the distance between them is changing after 2 minutes. Knowledge Check-in The function f is defined by f (x) = x e2x. It can be shown that f (n) (x) = (2n x + n 2n−1) e2x for all n+, where f (n) (x) represents the nth derivative of f (x). (a) By considering f (n) (x) for n =1 and n = 2, show that there is one minimum point P on the graph of f, and find the coordinates of P. (7) (b) Show that f has a point of inflexion Q at x = −1. (5)