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Question:

Let f(x) = max{|x|, x², |x|} for |x| ≤ 2 and f(x) = 8 - 2x for 2 < |x| ≤ 4. Let S be the set of points in the interval (-4, 4) at which f is not differentiable. Then S?

Is an empty set

Equals {-2, -1, 0, 1, 2}

Equals {-2, -1, 1, 2}

Equals {-2, 2}

Solution:

f(x) = { 8 + 2x, -4 ≤ x < -2
{ x², -2 ≤ x ≤ -1
{ |x|, -1 < x < 1
{ x², 1 ≤ x ≤ 2
{ 8 - 2x, 2 < x ≤ 4
f(x) is not differentiable at x = -2, -1, 0, 1, 2 ⇒ S = {-2, -1, 0, 1, 2}.