The negative sign comes from
Then you multiply by the "inner function".
is the derivative.
Now factor out a 2.
Note that the function is not defined when (Why?)
Now from the factored expression for the derivative we see that the derivative is zero when .
To determine if it is a local maxima or local minima, you could use the second derivative test, or simply make a table.
Note that if you plug in values slighly less than 4, you get a positive derivative, and values slight larger than 4 gives you a negative. So must be a local maxima.
You also see that the derivative goes off to infinity as x approaches 2 and 6.
Hi furor celtica
To find the gradient, just substitute the desired value of x to .
Example : If you want to find the gradient at x= 1, subs. the value to
To find turning points, set . Then, you'll get :where did the power of two go in the beginning of this explanation?