### Home > CALC > Chapter 8 > Lesson 8.2.2 > Problem 8-81

8-81.

**Multiple Choice:**The maximum value of*f*(*x*) =*x*(*x*− 3)(*x*− 7) on the interval 0 ≤*x*≤ 7 is nearest to: Homework Help ✎8

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Expand *f* before differentiating.

Remember that a maximum value is a *y*-value, not an *x*-value.

Notice that this is a CLOSED domain: 0 ≤ *x* ≤ 7.

Since maxima can exist where *f* '(*x*) = 0 or where *f* '(*x*) = DNE, it is important to check the *y*-values at each endpoint. *f*(0) = ________ and *f*(7) = ________

After all, an endpoint might exceed the *y*-values where *f* '(*x*) = 0; in which case, that endpoint will be in the global maximum.