How do I find the stationary points of a curve?
For a curve where y = f(x) the gradient of the curve is the derivative of this equation dy/dx. Stationary points of a curve occur when the gradient of the curve is zero. Hence find the expression for dy/dx and solve the equation:
dy/dx = 0
Once the x values which satisfy this equation are found the corresponding y values for each x value can be found by subbing the x values into the equation of the curve. You now have the full set of coordinates for the stationary points of the curve.
A possible extension would be to explain how the nature of the stationary points are found.
AM
Related Maths A Level answers
All answers ▸A curve has the equation x^2+2y^2=3x, by differentiating implicitly find dy/dy in terms of x and y.
Differentiate x^2+6x+1
Solve these simultaneous equations: 2x+y-5=0 and x^2-y^2=3
y(x) = x^2(1-x)e^-2x , find y'(x) in the form of g(x)e^-2x where g(x) is a cubic function to be found