Let f(x) = x³ - 10, x= [-15√3, 15√3]. Find the value of c guaranteed by the Mean Value Theorem on the interval [-15√3, 15√3] such that d dx f(x)|x=c f(15√3)-f(-15√/3) 15√3-(-15√3) Write your answers in ascending order separated by a comma. c = _
Let f(x) = x³ - 10, x= [-15√3, 15√3]. Find the value of c guaranteed by the Mean Value Theorem on the interval [-15√3, 15√3] such that d dx f(x)|x=c f(15√3)-f(-15√/3) 15√3-(-15√3) Write your answers in ascending order separated by a comma. c = _
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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![Let
\( f(x) = x^3 - 10, \quad x \in [-15\sqrt{3}, \, 15\sqrt{3}]. \)
Find the value of \( c \) guaranteed by the Mean Value Theorem on the interval \([-15\sqrt{3}, \, 15\sqrt{3}]\) such that
\[
\frac{d}{dx} f(x) \bigg|_{x=c} = \frac{f(15\sqrt{3}) - f(-15\sqrt{3})}{15\sqrt{3} - (-15\sqrt{3})}.
\]
Write your answers in ascending order separated by a comma.
\( c = \_ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1467f162-7185-45ab-925a-2589d3c8cce7%2Fb4579394-4c0a-4664-a39c-189d4b564347%2Fdrroq7hx_processed.png&w=3840&q=75)
Transcribed Image Text:Let
\( f(x) = x^3 - 10, \quad x \in [-15\sqrt{3}, \, 15\sqrt{3}]. \)
Find the value of \( c \) guaranteed by the Mean Value Theorem on the interval \([-15\sqrt{3}, \, 15\sqrt{3}]\) such that
\[
\frac{d}{dx} f(x) \bigg|_{x=c} = \frac{f(15\sqrt{3}) - f(-15\sqrt{3})}{15\sqrt{3} - (-15\sqrt{3})}.
\]
Write your answers in ascending order separated by a comma.
\( c = \_ \).
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