Math  /  Calculus

QuestionIdentify the true statement about the function f(x)=(x3)(x7)2f(x)=(x-3)(x-7)^{2} from the options given.

Studdy Solution
According to the second derivative test, if f(x)>0f''(x) >0, then f(x)f(x) has a relative minimum at that point. If f(x)<0f''(x) <0, then f(x)f(x) has a relative maximum at that point.
So, (3,0)(3,0) is a zero and a relative maximum, and (7,0)(7,0) is a zero and a relative minimum.
Therefore, the correct answer is option b. "(3,0)(3,0) is a zero and a relative maximum."

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