Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below. ____________ ≤ f(6) - f(2) ≤ ____________
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Originally Posted by topher0805 Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below. ____________ ≤ f(6) - f(2) ≤ ____________ $\displaystyle f(6)-f(2) = f'(c)(6-2)\implies 16\leq f(6)-f(2)\leq 20$. By the Mean Value Theorem. (Here $\displaystyle c\in (2,6)$).
Thanks for the help. Just to clarify, since 6-2 is 4, you multiplied both sides of the original inequality by 4 so that you had f(6)-f(2) by itself in the middle?
Originally Posted by topher0805 Thanks for the help. Just to clarify, since 6-2 is 4, you multiplied both sides of the original inequality by 4 so that you had f(6)-f(2) by itself in the middle? Exactly. you are on your way to be a math professor.
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