SOLUTION: Can not grasp the concept make no sense to me. I really need help with this one. Find the intervals where f is increasing, and the intervals where f is decreasing. 2x^2

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Question 726939: Can not grasp the concept make no sense to me. I really need help with this one. Find the intervals where f is increasing, and the intervals where f is decreasing. 2x^2 - 12x + 19.

Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Recognize that the polynomial is the function of a parabola so it will have either a minimum or maximum point. The polynomial here has a minimum point. Can you find this point (the vertex)? Alternatively, can you find (Real) zeros where the function crosses the x-axis? The x value of the vertex would be directly in the middle of them. The the left of the vertex as x approaches the vertex, the function is decreasing. To the right of the vertex as x tends to the right, the function is increasing.

In case the function does not have Real zeros, you can still convert to standard form (by completing the square) and find the vertex.

I did not solve the problem for you but gave guidance so that you might be able to solve the problem on your own.

SOLUTION: Can not grasp the concept make no sense to me. I really need help with this one. Find the intervals where f is increasing, and the intervals where f is decreasing. 2x^2 - 12x + 19.