Helpppppp (1 Viewer)

[Spina92]

How do i look at a graph and tell its minimum and maximum turning points, how do i use the formula's to tell the difference?

if you could send an email to whatfor92@hotmail with the answer to this question it would be greatfully appreciated.

P.S; is it true that the people who do Advanced Maths get NO formula sheet in the HSC Exam??????

 

[Makro]

Find the axis of symmetry: x = -b/2a.

Sub x into the original equation.

Min turning point = positive.
Max turning point = negative.

 

[AlexJB]

Have you done calc yet? Turning points exist when y' = 0. Find the values of x that satisfy that equation and then sub them into y''. If y'' > 0, its concave up with a min. turning pt. If y''<0, its concave down with a max turning point.

 

[gurmies]

If y" = 0, it's a point of inflexion. Sometimes you find the first derivative and you go to sub those potential turning points into the second derivative and get y'' = 0. This is an inconclusive case, and you have to test gradients before and after that x value to determine whether it's a horizontal point of inflexion or a turning point.

 

[bored of sc]

Maximum turning point: y' = 0, y'' < 0

Minimum turning point: y' = 0, y'' > 0

Also first derivate tests requires testing either side of x-value of stationary point to check for gradient. The left side is a value less than the stationary point x-value while the right side is greater. The table looks like this:
x <x-value x-value >x-value
y' + 0 - <-- Maximum
y' - 0 + <-- Minimum