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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