Lagrange Theorem

swisshome

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May 17, 2019
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I've got the following exercise to solve. Using Lagrange Theorem for the function f(x)=[MATH]sqrt(x)[/MATH] for a=1, and b=9. Find the value of x=c.
Now I checked the conditions.
1) f(x) is continuous on [1,9]
2) f(x) is differentiable on (1,9)
Hence, f'(c)=1/4
Now how to find c if f'(c)=1/4?
f(c)=1/4x+C if I'm right
 
I've got the following exercise to solve. Using Lagrange Theorem for the function f(x)=[MATH]sqrt(x)[/MATH] for a=1, and b=9. Find the value of x=c.
Now I checked the conditions.
1) f(x) is continuous on [1,9]
2) f(x) is differentiable on (1,9)
Hence, f'(c)=1/4
Now how to find c if f'(c)=1/4?
f(c)=1/4x+C if I'm right
Your last line is incorrect. You have [MATH]f(x) = \sqrt x[/MATH]. What is [MATH]f'(x)[/MATH]? Set [MATH]f'(x)=4[/MATH] and solve for [MATH]x[/MATH] to get [MATH]c[/MATH].
 
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