Curve Sketching (1 Viewer)

[angelxtearz]

Is the turning pt the pt of inflexion? dunno juz started this topic

1. Find the turning point on the curve f(x)=x^2 - 3x - 4 and determine the type (?) . Find the intercepts on the axes and sketch the curve.

 

[webby234]

d/dx(x^2 - 3x - 4)

= 2x - 3

For st. pts d/dx = 0

2x - 3 = 0
x = 1.5

The second derivative = 2 which means the curve is concave up for all values of x, which means the stationary pt is a minimum stationary point.

The turning point is not a point of inflexion - parabolas don't have them.
For points of inflexion, the concavity changes.

 

[Riviet]

I love my new printer. Hope the sketch helps.

 

[vizman]

sorry, is the point of inflexion the one where it hits the axis and immediately turns back the other way

 

[pLuvia]

The point of inflexion is the point where there is change in concavity of a graph.

Eg, in y=x³, the change in concavity is at (0,0)

 

[Riviet]

The point of inflexion is the point where there is change in concavity of a graph.

Eg, in y=x³, the change in concavity is at (0,0)

Just adding on an explanation to the example, for x<0 the curve is concave down (shaped like an n).
For x>0 the curve is concave up (shaped like a u). At x=0, the curve is stationary, and hence where the concavity changes from concave down to concave up.

 

[sando]

a turning point is a POSSIBLE point of inflexion (our teacher made sure we didnt forget this)

make sure you test for a point of inflexion and dont jsut assume