Differentiation

Question

A) a graph shows a part of the curve with the equation y - 2x²(x-3).

A) find the co-ordinates of the stationary points on the graph and determine the nature.

B) state the range of values of K for which Y=K intersects the graph at three distinct points.

can some one please help I am really stuck

Answer 1

y = 2x³ - 6x²

 

 

A)

 

Set the derivative of y equal to zero.

 

6x² - 12x = 0

 

Solve for x.

 

6x(x - 2) = 0

 

x = 0         and         x = 2

 

 

The coordinates are (0, 0)  and (2, -8).  This is where the slope of the tangent line to the curve is zero.  A horizontal line.  And these are the extreme points.

 

 

B)

 

If we look at the y coordinates extreme points, we can get our range. 

 

-8 < K < 0

 

Any value outside this range is where the horizontal line intersects the curve less than three times.