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Page 1 Math 151-copyright Joe Kahlig, 13C Challenge Problem: 1) Use any method to find the derivative of g(x) = |2x + 5| Note: Since we are taking the absolute value of a linear function, we know that g(x) is a continuous function and will have a sharp point at x = −2.5. As a piecewise defined function we know that g(x) = Thus g′ (x) = 2 if x ≥ −2.5 −2 if x < −2.5 2x + 5 −(2x + 5) if x ≥ −2.5 if x < −2.5