The function $f ( x ) = x ^ { 2 } - 6 x + 13$ satisfies the hypotheses of Rolle's Theorem on the interval $[ 0,6 ]$. Find all values of $c$ that satisfy the conclusion of the theorem.
A) 2,4
B) 2
C) 3,4
D) 3

Question

Quizplus · Accepted Answer

Rolle's Theorem requires that $f(a) = f(b)$. Here, $f(0) = f(6) = 13$, so the theorem applies. The derivative $f'(x) = 2x - 6$. Setting $f'(c) = 0$ gives $2c - 6 = 0$, so $c = 3$.

The Function f(x)=x2−6x+13f ( x ) = x ^ { 2 } - 6 x + 13f(x)=x2−6x+13

The Function $f ( x ) = x ^ { 2 } - 6 x + 13$