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Determine if the equation describes an increasing or decreasing function or neither.$$v(x)=4 x^{2}+1, x \geq 0$$

Increasing

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

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Determine if the equation …

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Determine whether the func…

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Determine whether each fun…

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So if we want to determine if a functions increasing or decreasing, one way to go about it is to look at the first derivative. So if the first derivative is positive, then we know will always be increasing. If the first derivative is always negative, then we will know it is always decreasing. So let's go ahead and first just take the derivative this, and keeping in mind that we have X is greater than or equal to zero. So take the derivative here. Eso if we do the powerful for this, subtract off one we get the prime affects is you go to eight X, and then the derivative of one is just zero. So we get. This is so now. The thing we have to keep in mind is that X is greater than or equal to zero. So if X is greater than or equal to zero, qualify would just multiply it side by eight. Then that implies eight X is greater than or equal to zero, which, that would say are derivative is either always positive or zero, which would imply that V of X is increasing. So I know it's a little bit different from what I have written up there where strictly larger than zero always, Um, but as long as it's not ever going to be decreasing at any point and it's equal to zero, we can also use that as saying it is increasing as well.

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