Consider the piecewise defined function Find the values of a and b that make the following function continuous. g(x) x² + ax+ 36 -x²+5a if x < 2 -{ if x > 2 Use the limit definition of the derivative to determine all possible values of a and b that make g into a differentiable function at x =2. What is the value of b? (You do not need to enter the value of a.) Enter your answer as a decimal. Round to three decimal places (as needed).
Consider the piecewise defined function Find the values of a and b that make the following function continuous. g(x) x² + ax+ 36 -x²+5a if x < 2 -{ if x > 2 Use the limit definition of the derivative to determine all possible values of a and b that make g into a differentiable function at x =2. What is the value of b? (You do not need to enter the value of a.) Enter your answer as a decimal. Round to three decimal places (as needed).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Transcribed Image Text:Consider the piecewise defined function Find the values
of a and b that make the following function continuous.
g(x)
x² + ax+
36
{
if x > 2
-x²+5a if x < 2
Use the limit definition of the derivative to determine all
possible values of a and b that make g into a
differentiable function at x =2.
What is the value of b? (You do not need to enter the
value of a.)
Enter your answer as a decimal. Round to three decimal
places (as needed).
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