Is #f(x)=-7x^3+x^2-2x-1# increasing or decreasing at #x=-2#?
2 Answers
See explanation.
Explanation:
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
Explanation:
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
As