3.2 Practice Flashcards
0
Q
Determine whether Rolle’s Theorem can be applied:
f(x) = cos(2x) [-π, π]
If it can, find the value of c guaranteed by the theorem.
A
Rolle’s Theorem applies.
c = -π/2, 0, π/2
1
Q
Determine whether Rolle’s Theorem can be applied:
f(x) = x^(2/3) - 1 [-8, 8]
If it can, find the value of c guaranteed by the theorem.
A
No, Rolle’s Theorem doesn’t apply. f(x) is not differentiable at x=0
2
Q
Determine whether the MVT can be applied:
f(x) = x^4 - 8x [0, 2]
If it can, find the value of c guaranteed by the theorem.
A
MVT applies
c = 2^(1/3)
3
Q
Determine whether the MVT can be applied:
f(x) = | 2x + 1 | [-1, 3]
If it can, find the value of c guaranteed by the theorem.
A
No, MVT doesn’t apply. f(x) is not differentiable at x = -1/2
