# What are the local extrema, if any, of #f (x) =80+108x-x^3 #?

##### 1 Answer

#### Answer:

We have a local minima at

#### Explanation:

A maxima is a high point to which a function

Further, as the tangents to the left of maxima will be sloping upwards, then flattening and then sloping downwards, slope of the tangent will be continuously decreasing, i.e. the value of second derivative

A minima on the other hand is a low point to which a function falls and then rises again. As such the tangent or the value of

But, as the tangents to the left of minima will be sloping downwards, then flattening and then sloping upwards, slope of the tangent will be continuously increasing or the value of second derivative

As

or

Now

at

and at

However, as elsewhere,

graph{80+108x-x^3 [-20, 20, -700, 700]}