How do I determine if a stationary point on a curve is the maximum or minimum?
If you are comfortable with differentiation. You can take the second derviatve of the equation of the cruve and plug in the x value of the curve. Based on this answer you can determine if it's a maximum, minimum or stationary. A maximum would have a negative value, a minimum a positive and stationary 0. If however you are not comfortable with this method and cannot memorize the different cases you can always substitute a point slightly before and after the point you're interested in. For example if you're considering x =3. You can subsitute 2.5 and 3.5 into your derivative and based on the signs draw a diagram representing the shape of the curve.
ES
Answered by Eryk S. • Further Mathematics tutor
3040 Views
See similar Further Mathematics GCSE tutorsRelated Further Mathematics GCSE answers
All answers ▸Work out the gradient of the curve y=x^3(x-3) at the point (3,17)
A curve has equation y = x^2 - 7x. P is a point on the curve, and the tangent to the curve at P has gradient 1. Work out the coordinates of P.
A particle is moving in a straight line from A to B with constant acceleration 4m/s^2. The velocity of the particle at A is 3m/s in the direction AB. The velocity of the particle at B is 18m/s in the same direction/ Find the distance from A to B.
If the equation of a curve is x^2 + 9x + 8 = y, then differentiate it.