(x+b, x≤1 16. f(x) = ax², x>1' Let f is the function given above. What are all the values of a and b for which f is differentiable at x=1? A. a = and b=== = and b and b is any real number B. a = and b == D. a=b+1, where b is any real number
(x+b, x≤1 16. f(x) = ax², x>1' Let f is the function given above. What are all the values of a and b for which f is differentiable at x=1? A. a = and b=== = and b and b is any real number B. a = and b == D. a=b+1, where b is any real number
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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![**Question 16**
Let \( f(x) \) be the function given by:
\[
f(x) =
\begin{cases}
x + b, & x \leq 1 \\
ax^2, & x > 1
\end{cases}
\]
Determine all values of \( a \) and \( b \) for which \( f \) is differentiable at \( x = 1 \).
**Options:**
A. \( a = -\frac{1}{2} \) and \( b = -\frac{1}{2} \)
B. \( a = \frac{1}{2} \) and \( b = \frac{3}{2} \)
C. \( a = -\frac{1}{2} \) and \( b \) is any real number
D. \( a = b + 1 \), where \( b \) is any real number](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F981166fe-4516-4e5d-91f3-95cacb37d8bb%2Fb4020aa3-eb7e-4dd0-8342-f610beac7d18%2Ftr3gmnc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 16**
Let \( f(x) \) be the function given by:
\[
f(x) =
\begin{cases}
x + b, & x \leq 1 \\
ax^2, & x > 1
\end{cases}
\]
Determine all values of \( a \) and \( b \) for which \( f \) is differentiable at \( x = 1 \).
**Options:**
A. \( a = -\frac{1}{2} \) and \( b = -\frac{1}{2} \)
B. \( a = \frac{1}{2} \) and \( b = \frac{3}{2} \)
C. \( a = -\frac{1}{2} \) and \( b \) is any real number
D. \( a = b + 1 \), where \( b \) is any real number
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