Determine the largest open interval of the domain (a) over which ...

Question

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = -(x - 2)^2 - 5

Accepted Answer

Consider the function F of X is equals to negative X minus four squared plus six and find the largest open interval of the domain at which the function is increasing and decreasing. Well, we have the vertex form of a parabola to B Y is equals to a multiplied by X minus H squared plus K. Now we notice our tablet is actually already in this form, we can then say our H will be equals to four K will be equals to six making our vertex for six like so now that we have this, we're gonna test some values of X. You wanna see what the resulting function value is. Let's test one value greater than four and one value less than four. Let's say we use three and five. Let's take F of three, for instance, that would be negative three minus four squared plus six, which simplifies the fact fa five similarly will simplify to five. Now we notice our resolving function values are both less than our vertex Y value six. Because that's the case, we can determine this is a downward facing parabola. And because it's downward facing, we will be increasing from negative infinity. So we get to our vertex and decreasing from our vertex to positive infinity. We gonna say increasing some negative infinity to four, decreasing will be then from 4 to infinity, we can then conclude the answer to our problem as answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = -(x - 2)^2 - 5

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