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
3085 Views
See similar Further Mathematics GCSE tutorsRelated Further Mathematics GCSE answers
All answers ▸The circle c has equation x^2+ y ^2=1 . The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.
Show that (n^2) + (n+1)^2 + (n+2)^2 = 3n^2 + 6n + 5, Hence show that the sum of 3 consecutive square numbers is always 2 away from a multiple of 3.
Rationalise and simplify (root(3) - 7)/(root(3) + 1) . Give your answer in the form a + b*root(3) where a, b are integers.
A curve has equation y = ax^2 + 3x, when x= -1, the gradient of the curve is -5. Work out the value of a.