Lagrange Theorem

swisshome

New member
I've got the following exercise to solve. Using Lagrange Theorem for the function f(x)=$$\displaystyle sqrt(x)$$ 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

LCKurtz

Junior Member
I've got the following exercise to solve. Using Lagrange Theorem for the function f(x)=$$\displaystyle sqrt(x)$$ 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 $$\displaystyle f(x) = \sqrt x$$. What is $$\displaystyle f'(x)$$? Set $$\displaystyle f'(x)=4$$ and solve for $$\displaystyle x$$ to get $$\displaystyle c$$.