A curve has equation y = x^3 - 6x^2 - 15x. The curve has a stationary point M where x = -1. Find the x-coordinate of the other stationary point on the curve.
A stationary point can be found when dy/dx = 0. The first thing we need to do is differentiate y to find dy/dx, and solve it for dy/dx = 0. This gives usdy/dx = 3x2 - 12x - 15 = 0 = (3x + 3)(x - 5) = 0 (using quadratic formula)Therefore x = -1 and x = 5.The question already gives us x = -1, so the answer is x = 5.
EG
Related Maths A Level answers
All answers ▸Find the integral of 4x^2 - 10x + 1/(x^(1/2)), with respect to x, in its simplest form.
A fair die has six faces numbered 1, 1, 1, 2, 2, and 3. The die is rolled twice and the number showing on the uppermost face is recorded. Find the probability that the sum of the two numbers is at least three.
A curve has parametric equations x = 2 sin θ, y = cos 2θ. Find y in terms of x
A cannonball is fired at an angle of 30 degrees and a velocity of 16 m/s. How long does it take (to 2 significant figures) for the cannonball to reach the ground?