Is #f(x)=-7x^3+x^2-2x-1# increasing or decreasing at #x=-2#?
To find if a function is increasing or decreasing at a given point we have to calculate its derivative at the point.
The function is:
so its derivative is:
The value of derivative at
The value of the derivative is less than zero, so the function is decreasing.
Either drawing the graph or taking the derivate
Let's start by drawing the graph in Geogebra (an excellent, free geometry program):
Looking at it , it is quite clear that
We can also find this without drawing the graph by taking the derivate, which gives the slope of the tangent in each value of x:
Insert the value