How do you find stationary points of an equation, eg. y=x^2+3x+2
Stationary points of an equation are found where the gradient of the tangent at this point equals zero. A diagram can illustrate this. To find them differentiate the given equation (which gives the gradient) and set this to zero. eg. dy/dx = 2x+32x+3=0x=-3/2Plug this back into the equation of the line to find the y valuey=(-3/2)^2 + 3(-3/2) +2y= -1/4Stationary point is (-3/2, -1/4)To find the nature of this stationary point, find the second derivative, plug in your x value. If the value of the second derivative if positive, the point is a minimum, negative means a maximum.
EC
Related Maths A Level answers
All answers ▸A curve is defined by the parametric equations x = 3^(-t) + 1, y = 2 x 2^(t). Show that dy\dx = -2 x 3^(2t).
What is a derivative?
Given that y = 4x^3 – 5/(x^2) , x not equal to 0, find in their simplest form (a) dy/dx, and (b) integral of y with respect to x.
Find all solutions of the equation in the interval [0, 2π]. 5 cos^3 x = 5 cos x