1.) The function defined below satisfies Rolle\'s Theorem on the given interval.
ID: 2827842 • Letter: 1
Question
1.)
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval where f'(c)=0.
f(x) = x3 - 4x2 + 4x, [0, 2]
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval where f'(c)=0.
f(x) = x + 12x-1 , [-4, -3]
f(x) = x3 - 1.2x , [1, 2]
The function defined below satisfies the Mean Value Theorem on the given interval. Find the value of c in the interval where f'(c)=(f(b) - f(a))/(b - a).
f(x) = 1.3x-1 + 1.1 , [1, 2]
Explanation / Answer
1.
f'(x) = 3x^2 -8x +4=(x-2)(3x-2)=0
c = 2/3
2.
f'(x) = 1-12/x^2 = 0
c = -2sqrt(3)
3.
f'(x) = 3x^2-1.2 = 5.8/1 = 5.8
=>
c = sqrt(7/3) = 1.527
4.
f'(x) = -1.3/x^2 = -0.65
=>
c = sqrt(2) =1.414
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