LimitsHard
Question
Let f(x) = x3 - x2 + x + 1 and g(x) = 
, then:
, then:Options
A.g(x) is continuous & derivable at x = 1
B.g(x) is continuous but not derivable at x = 1
C.g(x) is neither continuous nor derivable at x = 1
D.g(x) is derivable but not continuous at x = 1
Solution
f(x) = x3 - x2 + x + 1
f′(x) = 3x2 - 2x + 1 > 1 ∀ x ∈ R
f(x) is strictly increasing
So g(x) =
g(1) = f(1) = 1 - 1 + 1 + 1 = 2 =
= 3 - 1 + 1 = 3
g(x) is neither continous nor differentiable at x = 1
f′(x) = 3x2 - 2x + 1 > 1 ∀ x ∈ R
f(x) is strictly increasing
So g(x) =
g(1) = f(1) = 1 - 1 + 1 + 1 = 2 =
= 3 - 1 + 1 = 3g(x) is neither continous nor differentiable at x = 1
Create a free account to view solution
View Solution Free