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Determine if the equation describes an increasing or decreasing function or neither.$$s(x)=-2 x^{2}+6, x \leq 0$$

Increasing

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Missouri State University

McMaster University

Harvey Mudd College

Baylor University

Lectures

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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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if we want to determine if this function is always increasing or decreasing, One way to go about it is to take the derivative of it and then see if it will always be positive or negative. It is always positive. Then weaken. Say it will always be increasing. And if it's always negative, then we say will always be decreasing. So let's go ahead and take the derivative of this. First on, well, keep in mind that X is less than or equal to zero, because this will be important. But, um yeah, so we take the derivative here, so we need power rules to move that outfront subtract off. One we get s prime effects is equal to negative four X, um and then derivative of sex is just zero. So we end up with this here and with the stipulation that X is less than zero. So if we know X is always a certain zero, if we multiply this by negative four, that's going to implies we have negative for X is going to be greater than or equal to zero now and well, this is our derivative. So that's going to imply that SFX is increasing. And so I know here this is saying that the derivative is greater than or equal to zero and up top here we just say strictly, Um, but it's okay if it is equal to zero, because the actual definition of increasing is just that it is like f of a less than ffb kind of like that. And if we always have this going on, then it would always be increasing. Eso This isn't always necessarily captured in this definition, so that's what I'm saying. Here it's OK that we have equal to zero, um, as opposed to just strictly larger that

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