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
3329 Views
See similar Further Mathematics GCSE tutorsRelated Further Mathematics GCSE answers
All answers ▸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.
Given that xy=2 and y=3x+5, find x and y. Do not use trial and improvement.
A=(1,a;0,1/2) B=(1,-1;0,2) AB=I, calculate the value of a.
If y=x^3+9x, find gradient of the tangent at (2,1).