The function f(x)=x^2 -2x -24x^(1/2) has one stationary point. Find the value of x when f(x) is stationary, and hence determine the nature of this stationary point.
dy/dx = 2x - 2 -12x-1/2dy/dx = 02x - 2 - 12x-1/2 = 0x = 4 (stationary point)d2y/dx2= 2 + 6x-3/2when x=4, d2y/dx2= 11/411/4 > 0 therefore the point is a minimum
Related Maths A Level answers
All answers ▸Find the roots of the equation y=x^2-8x+5 by completing the square.
A particle, P, moves along the x-axis. At time t seconds, t > 0, the displacement, is given by x=1/2t^2(t ^2−2t+1).
Given that y={(x^2+4)(x−3)}/2x, find dy/dx in its simplest form.
How would you express (11+x-x^2)/[(x+1)(x-2)^2] in terms of partial fractions?