SOLUTION: Given -x^2-6x-3, is the vertex a maximum or minimum for the function? What is the value fo that maximum or minimum?
There is nothing in my book about maximums and minimums, plea
Question 138228: Given -x^2-6x-3, is the vertex a maximum or minimum for the function? What is the value fo that maximum or minimum?
There is nothing in my book about maximums and minimums, please help! Answer by solver91311(24713) (Show Source):
is a parabola that opens upward when or downward when (and is no longer a parabola if ). Your value for a is -1, so the parabola opens downward and the vertex is then a maximum.
The x-coordinate of the vertex is given by , so for your function: . The value of the function at that point is .
Calculus solution:
A continuous function has a local extrema wherever the first derivitive is equal to zero. It is a maximum if the 2nd derivitive is negative at that point and a minimum if the 2nd derivitive is positive at that point.
=>
Let => local extrema at , and the value of the function at that point is found the same way as in the algebra solution: .
=> the 2nd derivitive is everywhere negative, so the local extreme point is a maximum.
