A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.
(a) i) dy/dx= 2x-2-12x-1/2ii) d2 y/dx2 = 2+6x-3/2(b) Substitute x=4 into dy/dx= 2x-2-12x-1/2 Show that dy/dx= 0 and state 'hence there is a stationary point' (c) Substitute x=4 into d2 y/dx2 = 2+6x-3/2 (=2.75) d2 y/dx2>0 and state 'hence minimum'
