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If f(a) = f(b) = 0 and f(x) is continuous on [a, b], then
f(x) must be identically zero
f ′(x) may be different from zero for all x on [a, b]
there exists at least one number c, a < c < b, such that f ′(c) = 0
f ′(x) must exist for every x on (a, b)
none of the preceding is true
Suppose y = f(x) = 2x^3 − 3x. If h(x) is the inverse function of f, then h′
(−1) =
−1
1
3
Suppose f(1) = 2, f ′(1) = 3, and f ′(2) = 4. Then (f −^1 )′(2)
equals −
equals −
equals
equals
cannot be determined
If f(x) = x^3 − 3x^2 + 8 x + 5 and g(x) = f −^1 (x), then g′(5) =
8
1
53
Suppose . It follows necessarily that
g is not defined at x = 0
g is not continuous at x = 0
the limit of g(x) as x approaches 0 equals 1
