Epsilon-delta Challenge

Calculus Level 1

For the function f(x)=3x2+2x+1,f(x) = 3x^2 + 2x + 1, Alice wants Bob to show that limx2f(x)=17\displaystyle \lim_{x \rightarrow 2} f(x) = 17 using the ε\varepsilon-δ\delta definition of a limit.

Alice says, "I bet you can't choose a real number δ\delta so that for all xx in (2δ,2+δ)(2 - \delta, 2 + \delta), we'll have that f(x)17<0.5\left|f(x) - 17\right| < 0.5."

Which of the following four choices is the largest δ\delta that Bob could give so that he completes Alice's challenge?

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