anonymous
  • anonymous
Determine if the function f(x)=4x√−3x satisfies the Mean Value Theorem on [1, 25]. If so, find all numbers c on the interval that satisfy the theorem.
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
Find f'(x) Find the slope of the secant Set, f'(x)=slope of secant
SolomonZelman
  • SolomonZelman
Find: f(1) and f(5), and then the slope between x=1 and x=5.
SolomonZelman
  • SolomonZelman
Differentiate the f'(x).

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SolomonZelman
  • SolomonZelman
Set f'(x)=slope between x=1 and x=5.
SolomonZelman
  • SolomonZelman
want example?
SolomonZelman
  • SolomonZelman
\(\color{#000000 }{ \displaystyle f(x)=4x^2-6x }\), on \([2,10]\). \(\color{#000000 }{ \displaystyle f(2)=4 }\) \(\color{#000000 }{ \displaystyle f(10)=340 }\) \(\color{#000000 }{ \displaystyle {\rm Slope }=\frac{\Delta y}{\Delta x} =\frac{f(10)-f(2)}{10-2} }\) \(\color{#000000 }{ \displaystyle {\rm Slope }=\frac{340-4}{8} =\frac{336}{8} =42}\) That was the "slope of the secant". Now the derivative-slope; \(\color{#000000 }{ \displaystyle f'(x)=(2)4x^{2-1}-(1)6x^{1-1} }\) \(\color{#000000 }{ \displaystyle f'(x)=8x-6}\) this is your slope-generator. (right?) So, you want to find the points on the function that will have the same slope as the slope of the secant. \(\color{#000000 }{ \displaystyle 42=8x-6}\) \(\color{#000000 }{ \displaystyle x=6}\) (this is the conclusion of the MVT)

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