Identify the interval(s) where h is differentiable. For each point where h is not differentiable, state why. h(x) = (-3x² - 8x - 10, x < -3 10x + 3, -3

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Problem Statement:

**Identify the interval(s) where \(h\) is differentiable. For each point where \(h\) is not differentiable, state why.**

### Given Function:

\[ h(x) = \begin{cases} 
-3x^2 - 8x - 10, & x < -3 \\
10x + 3, & -3 \le x < 0 \\
3e^x, & x \ge 0
\end{cases} \]
Transcribed Image Text:### Problem Statement: **Identify the interval(s) where \(h\) is differentiable. For each point where \(h\) is not differentiable, state why.** ### Given Function: \[ h(x) = \begin{cases} -3x^2 - 8x - 10, & x < -3 \\ 10x + 3, & -3 \le x < 0 \\ 3e^x, & x \ge 0 \end{cases} \]
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