If I have the equation of a curve, how do I find its stationary points?
A stationary point is where the gradient of a curve momentarily stops changing.Let's take the example that we want to find the stationary points of the curve y=2x^5 - 5x^2. Find the derivative of the equation using the standard differentiation method. 2x^5 - 5x^2 would derive to 10x^4 - 10x. Then find the second derivative, by differentiating your first derivative in the same way. 10x^4 - 10x would become 40x^3 - 10. To find the stationary points, set the second derivative equal to 0, so in our example 40x^3 -10 = 0. Using this new equation, solve for x. In our case, solving for x gives us x^3=0.25 and therefore x=0.630 (3.s.f). If the question asks for it, you may need to find the y-coordinate by substituting the x-value back into the original equation- in this case we get y=1.789 (3.s.f).
Related Maths A Level answers
All answers ▸A ball is released on a smooth ramp at a distance of 5 metres from the ground. Calculate its speed when it reaches the bottom of the ramp.
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.
Find the derivative of x^x
Given f(x)=2x^3 - 2x^2 + 8x, find f'(x) and f"(x).