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Can the intermediate-value theorem be used to show there is a solution for the equation f(x)=0 on the interval [3,5] if f(x)=? Give an explanation why.

1 Answer

4 votes

The question is incomplete, so the complete question is:

Can the intermediate-value theorem be used to show there is a solution for the equation f(x)=0 on the interval [3,5] if f(x)=
\sqrt{3x^(2) - 7x} - 3? Give an explanation why.

(a) Yes, because f(3) > 0 and f(5) < 0

(b) No, because f(3) < 0 and f(5) < 0

(c) Yes, because f(3) < 0 and f(5) > 0

(d) No, because f(3) > 0 and f(5) > 0

The Intermediate-Value Theorem states that if a function is continuous over the interval [a,b], the function will take any value between f(a) and f(b) over the interval. For the function above, f(3) = - 1,55 and f(5) = 3,32.

So, in the interval, the curve of the function crosses the x-axis, which means there is a solution.

Therefore, the correct alternative for this question is C .