$($d$)$ Suppose f is continuous on $a,b.$ Then there is a point c in $(a,b)$ such that $f(c)=\frac{f(a)f(b)}{2}.$ Choose the correct answer below.

A$.$ The statement is false; $f(c)$ can never equal $\frac{f(a)f(b)}{2}$ in any function.

B$.$ The statement is true by the Intermediate Value Theorem.

C$.$ The statement is false; if $f(a)=f(b)$ and the function value at every point in the interval is either less than or greater than the function value at the endpoints, then $f(c)=f(a)=f(b),$ which would not exist in the interval $(a,b).$

D$.$ The statement is true; since c is in $(a,b)$ then it is always true that $\frac{f(a)f(b)}{2}$ is in $(a,b.$

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