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Let f(¹) = √2 +2. Since f(x) is differentiable on [-2, 7], by the Mean Value Theorem, we know there exists at least one c in the open interval (-2, 7) such that f'(c) is equal to the mean slope on the interval [ – 2,7]. This function has one such c. Find it using calculus. C = Now give the graphical representation of the Mean Value Theorem in this case: To do this, graph these three things: 1. f(1) = √2+2 2. The secant line through (-2, 0) and (7,3) and 3. The tangent line at the point, c, such that the tangent line is parallel to the secant line.

Let f(¹) = √2 +2. Since f(x) is differentiable on [-2, 7], by the Mean Value Theorem, we know there exists at least one c in the open interval (-2, 7) such that f'(c) is equal to the mean slope on the interval [ – 2,7]. This function has one such c. Find it using calculus. C = Now give the graphical representation of the Mean Value Theorem in this case: To do this, graph these three things: 1. f(1) = √2+2 2. The secant line through (-2, 0) and (7,3) and 3. The tangent line at the point, c, such that the tangent line is parallel to the secant line.

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter6: Polynomials
Section6.6: Divide Polynomials
Problem 6.176TI: Find the quotient: 25x38)(5x2) .
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5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 -3 Clear All Draw: 1 2 3 6 7 8
Transcribed Image Text:5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 -3 Clear All Draw: 1 2 3 6 7 8
Let f(x) = √√√x + 2. Since f(x) is differentiable on [-2, 7], by the Mean Value Theorem, we know there exists at least one c in the open interval (-2, 7) such that f'(c) is equal to the mean slope on the interval [ - 2, 7]. This function has one such c. Find it using calculus. c = Now give the graphical representation of the Mean Value Theorem in this case: To do this, graph these three things: 1. f(x)=√x+2 2. The secant line through (-2, 0) and (7,3) and 3. The tangent line at the point, c, such that the tangent line is parallel to the secant line.
Transcribed Image Text:Let f(x) = √√√x + 2. Since f(x) is differentiable on [-2, 7], by the Mean Value Theorem, we know there exists at least one c in the open interval (-2, 7) such that f'(c) is equal to the mean slope on the interval [ - 2, 7]. This function has one such c. Find it using calculus. c = Now give the graphical representation of the Mean Value Theorem in this case: To do this, graph these three things: 1. f(x)=√x+2 2. The secant line through (-2, 0) and (7,3) and 3. The tangent line at the point, c, such that the tangent line is parallel to the secant line.
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