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Determine if the equation describes an increasing or decreasing function or neither.$$h(x)=\sqrt{2 x+3}$$

Increasing

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Campbell University

Oregon State University

Idaho State University

Lectures

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Determine if the equation …

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Determine whether each fun…

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Graph the function . State…

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Determine whether the func…

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Inspect the graph of the f…

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So if we want to determine if this is going to be increasing or decreasing, what we can do is first take the derivative of this. And if the derivative is always positive, then we know it's increasing. If the derivative is always negative, then we know the function is decreasing. So let's go ahead and take the derivative of this. Uh so first, I'm actually rewrite this where it's a one half power, so we would use power rule. So we move the power outfront, subtract one off of this So this is going to first be one half two x plus three raise to the negative one half. But then remember, we have to do change rules. We take the throat of of the inside function, which is going to be two X plus three and then the derivative two X plus three. Well, the derivative of to excess to the derivative +30 So that's just going to be too. So actually, this, too, and that one half cancel so we would end up with 1/2 X plus to X plus three square rooted. And so this is a church prime of X and now notice that this is always going to be strictly larger than zero, since we know the square root of any number is going to be positive, Um, and then if we divide any positive number by one, that's still going to be positive. So this implies that h of X is increasing.

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