If #y= x^3 + 6x^2 + 7x -2cosx#, what are the points of inflection of the graph f (x)?
Here is the graph of it:
As you can see, it has an absolute maxima, an absolute minima, and a point of inflection that lies between the extremas.
Its roots are,
To find the
Here is the graph of this derivative function:
Its roots are
The point of inflection lies between these two extremas and can be found by taking the second derivative of your original function and setting it equal to zero, and solving for its root:
Here is the graph of this function:
It has one root,
to plug this into your original function and calculate
The above solution was arrived at by using graphing utilities. Without using graphing utilities, it would take some cumbersome algebra in the complex domain to solve for the above