7.5 CHAPTER 7. DIFFERENTIAL CALCULUS
More practice video solutions or help at http://www.everythingmaths.co.za(1.) 01fy (2.) 01fz (3.) 01g0Local Minimum, Local Maximum and Point
of Inflection
EMCBM
If the derivative (dydx) is zero at a point, the gradient of the tangent atthat point is zero. It means that a
turning point occurs asseen in the previous example.
1
2
3
4
5
6
7
8
9
− 1
− 1 1 2 3 4
y� � x� �( 1 , 0 )
( 3 , 4 )
( 4 , 0 )
From the drawing the point (1; 0) represents a local minimum and the point (3; 4) the local maximum.
A graph has a horizontal point of inflexion where the derivative iszero but the sign of thegradient
does not change. That means the graph will continue to increase or decrease after the stationary point.