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Determine if the equation describes an increasing or decreasing function or neither.$$g(x)=-4 x^{2}+1$$

Neither

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

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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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no. If we want to determine whether this is increasing or decreasing, what we can first do is take the derivative of it and then determine if F prime is always positive or always negative. If it's always positive, then we know it's increasing if it's always negative that we know it's decreasing. So let's go ahead and take the derivative of this S O G. Prime effects is going to be equal to so we would use power rules of power rules that's taking power. Move it out front. Tracked off one S O. That would be negative four times to some negative eight x plus zeroes. That's just negative. Eight x for derivative. Now, depending on what values would plug in for X, this will be positive or negative. So g prime of X equal to negative eight X is going to be larger than zero if X is less than zero. Because we were just divide over by negativity and then the sign would flip and G Prime of X is equal to negative. Alex is less than zero if X is greater than zero and again we just divide by negative eight and then the sign flips, so this implies that G of X is going to be neither increasing nor decreasing. Since we have, we're on some interval, it's decreasing. In some interval, it's increasing.

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