Applications of Differentiation (AQA GCSE Further Maths)

Point lies on the curve 

The -coordinate of is – 4.

Show that the equation of the normal to the curve at is .

The normal at also intersects the curve at .

Work out the -coordinate of.

is the point on the curve  where .

The gradient of the normal to the curve at is .

Work out the value of .

Show that has a minimum value when   .

is a point on a curve.

The curve has gradient function .

The tangent to the curve at is parallel to the line . Work out the -coordinate of .

The curve has .

The curve has exactly one stationary point at where .

Use the expression for  to show that is a minimum point.

A curve has equation .

At a point on the curve, the tangent is parallel to the line .

Work out the coordinates of .

You must show your working.

is the graph of a cubic function.

for

for

The function is

increasing for

decreasing for

increasing for

Draw a possible sketch of for values of from to

The continuous curve g()  has exactly two stationary points.

The stationary points are

• a maximum point at where and

•  a minimum point at

On the axes below, sketch the curve.

Label points and on your sketch.

Use differentiation to show that  is an increasing function for all values of .

The diagram shows a sketch of the cubic curve   

where is a constant.

The -axis is a tangent to the curve at its minimum point.

Work out the value of

The curve intersects the -axis at .

The tangent to the curve at intersects the -axis at .

Work out the length .

......................units