Generalized Mean Value Theorem Suppose the functions f and g are continuous on ⌈ a, b ⌉ and differentiable on ( a, b ) , where g ( a ) ≠ g ( b ) . Then there is a point c in ( a , b ) at which f ( b ) − f ( a ) g ( b ) − g ( a ) = f ′ ( c ) g ′ ( c ) . This result is known as the Generalized (or Cauchy’s) Mean Value Theorem. a. If g ( x ) = x , then show that the Generalized Mean Value Theorem reduces to the Mean Value Theorem. b. Suppose f ( x ) = x 2 − l, g ( x ) = 4 x + 2, and [ a , b ] = [0, 1]. Find a value of c satisfying the Generalized Mean Value Theorem.
Generalized Mean Value Theorem Suppose the functions f and g are continuous on ⌈ a, b ⌉ and differentiable on ( a, b ) , where g ( a ) ≠ g ( b ) . Then there is a point c in ( a , b ) at which f ( b ) − f ( a ) g ( b ) − g ( a ) = f ′ ( c ) g ′ ( c ) . This result is known as the Generalized (or Cauchy’s) Mean Value Theorem. a. If g ( x ) = x , then show that the Generalized Mean Value Theorem reduces to the Mean Value Theorem. b. Suppose f ( x ) = x 2 − l, g ( x ) = 4 x + 2, and [ a , b ] = [0, 1]. Find a value of c satisfying the Generalized Mean Value Theorem.
Solution Summary: The author explains the Generalized Mean Value Theorem when reduce to the Mean Valuation Theory for the given function. The function is g(x)=x.
Generalized Mean Value Theorem Suppose the functions f and g are continuous on ⌈a, b⌉ and differentiable on (a, b), where g(a) ≠ g(b). Then there is a point c in (a, b) at which
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This result is known as the Generalized (or Cauchy’s) Mean Value Theorem.
a. If g(x) = x, then show that the Generalized Mean Value Theorem reduces to the Mean Value Theorem.
b. Suppose f(x) = x2 − l, g(x) = 4x + 2, and [a, b] = [0, 1]. Find a value of c satisfying the Generalized Mean Value Theorem.
Can you please help me with finding the derivative of the function, I need to check whether the modulus of the derivative is non zero to check whether it is a curve or not
prove using mean value theorem
According to the Mean Value Theorem, if f (x) is a function that is continuous on
a, b , and is differentiable on (a, b), then there exists at least one point
CE (a, b) such that f' (c) is equal to the slope of the secant line passing through
the points (a, f (a)) and (b, f (b)) .
Consider the function f (t)
2t3
6t? + 8 on the interval [-1, 2]. Find the
= -
-
set of values of c for which such that f' (c) is equal to the slope of the secant line
passing through the points (-1, f (–1)) and (2, f (2)) . Use set roster notation
and round the elements to the nearest hundredth. Write elements in ascending
order.
Chapter 4 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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