# How do you find the intervals of increasing and decreasing using the first derivative given #y=-2x^2+4x+3#?

We want to perform that first derivative test here:

We begin by differentiate using the power rule:

Keep in mind that

Now we want to factor and set it equal to zero:

We create a test a interval from

Now you pick numbers in between the interval and test them in the derivative. If the number is positive this means the function is increasing and if it's negative the function is decreasing.

I picked 0 a number from the left

This means from

Then I picked a number from the right which was 2.

This means from

So, from

Note: For this exact reason we can say that there's an absolute max at

Attach is an image that may help you:

The graph will help you visualize it better.

graph{-2x^2+4x+3 [-10, 10, -5, 5]}

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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