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Chapter 7: Problem 51

Describe the \(x\) -values at which the function is differentiable. Explain your reasoning. $$ y=|x+3| $$

Short Answer

Expert verified
The function \(y = |x + 3|\) is differentiable for all real numbers except \(x = -3\).

Step by step solution

01

Identify the Corner Point

The function \(y = |x + 3|\) is not differentiable at \(x = -3\) since here the function changes direction abruptly, forming a corner. This is where the input of the absolute value function becomes zero.
02

Determine Range of Differentiability

Since the function \(y = |x + 3|\) is only non-differentiable at \(x = -3\), the function is differentiable for all other real numbers, \(-\infty < x < -3\) and \(-3 < x < \infty\).

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