Mean Value Theorem: If F is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) then there must exist at least one number c in (a, b) for which F'(c) = F(b)-F(a) b-a In problems 2 and 3 do the following: (a) Apply the Mean Value Theorem to the function: F(x) = x³ - 3x on the indicated interval I to find all numbers, c, in the interior of I, which satisfy the conclusion of this theorem. I.e., find all numbers e interior to I for which the average change in Fover I is equal to the instantaneous rate of change in F at c. (b) Sketch a graph of the function y = F(x) on the interval I and interpret your results from part (a) geometrically in terms of the appropriate tangent and secant lines to your graphs. 2. I [-1, +2] 3. I = [-1, +1]
Mean Value Theorem: If F is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) then there must exist at least one number c in (a, b) for which F'(c) = F(b)-F(a) b-a In problems 2 and 3 do the following: (a) Apply the Mean Value Theorem to the function: F(x) = x³ - 3x on the indicated interval I to find all numbers, c, in the interior of I, which satisfy the conclusion of this theorem. I.e., find all numbers e interior to I for which the average change in Fover I is equal to the instantaneous rate of change in F at c. (b) Sketch a graph of the function y = F(x) on the interval I and interpret your results from part (a) geometrically in terms of the appropriate tangent and secant lines to your graphs. 2. I [-1, +2] 3. I = [-1, +1]
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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
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![Mean Value Theorem:
If F is continuous on the closed interval [a, b] and differentiable on the open interval (a, b)
then there must exist at least one number c in (a, b) for which
F'(c) =
F(b)-F(a)
b-a
In problems 2 and 3 do the following:
(a) Apply the Mean Value Theorem to the function:
F(x) = x³ - 3x
on the indicated interval I to find all numbers, c, in the interior of I, which satisfy the
conclusion of this theorem. I.e., find all numbers e interior to I for which the average
change in Fover I is equal to the instantaneous rate of change in F at c.
(b) Sketch a graph of the function y = F(x) on the interval I and interpret your results from
part (a) geometrically in terms of the appropriate tangent and secant lines to your graphs.
2. I = [-1, +2]
3. I = [-1, +1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f989c57-8a7c-4041-9fe7-2f824b6b0127%2F20c46fa5-2a2c-412d-ae48-c5ca4b3198d3%2Frbpeqtm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Mean Value Theorem:
If F is continuous on the closed interval [a, b] and differentiable on the open interval (a, b)
then there must exist at least one number c in (a, b) for which
F'(c) =
F(b)-F(a)
b-a
In problems 2 and 3 do the following:
(a) Apply the Mean Value Theorem to the function:
F(x) = x³ - 3x
on the indicated interval I to find all numbers, c, in the interior of I, which satisfy the
conclusion of this theorem. I.e., find all numbers e interior to I for which the average
change in Fover I is equal to the instantaneous rate of change in F at c.
(b) Sketch a graph of the function y = F(x) on the interval I and interpret your results from
part (a) geometrically in terms of the appropriate tangent and secant lines to your graphs.
2. I = [-1, +2]
3. I = [-1, +1]
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