Verify Rolle's Theorem and then check for values of x that satisfy it.
f(x)=x−91x for interval [0,81]
f(x)=(x)1/2−91x
1st check: The function is differentiable and continuous over the interval, cause it's a polynomial.
f(0)=(0)1/2−91(0)=0
f(81)=(81)1/2−91(81)=0
2nd check
f(0)=f(81)
f′(x)=21u−1/2−91
f′(x)=21x−1/2−91
21x−1/2−91=0
21x−1/2=91
x−1/2=92
[x−1/2]−2=[92]−2
x= :?:
f(x)=x−91x for interval [0,81]
f(x)=(x)1/2−91x
1st check: The function is differentiable and continuous over the interval, cause it's a polynomial.
f(0)=(0)1/2−91(0)=0
f(81)=(81)1/2−91(81)=0
2nd check
f(0)=f(81)
f′(x)=21u−1/2−91
f′(x)=21x−1/2−91
21x−1/2−91=0
21x−1/2=91
x−1/2=92
[x−1/2]−2=[92]−2
x= :?:
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