Continuity and DifferentiabilityHard
Question
Let h(x) = min {x, x2} for every real number of x, then
Options
A.h is differentiable for all x
B.h is continuous for all x
C.h′(x) = 1, for all x > 1
D.h is not differentiable at two values of x,
Solution
From the figure.
h(x) is continuous all x, but h(x) is not differentiable at two points x = 0 and x = 1 (due to sharp edges). Also h′(x) = 1, ∀ x > 1
Hence (b),(c) and (d) is correct answers.
Create a free account to view solution
View Solution FreeMore Continuity and Differentiability Questions
If g is inverse of f and f(x) = x2 + 3x - 3 (x > 0) then g′(1) equals -...If f(x) = x + + .........., then (0) + f″(0) + ........ + f″″.....n times (0) is equal to -...Let f(x) = then -...If a function f (x) is defined as f(x) = , then -...If f(x) = | (x - 4)(x - 5) | , then f′(x) is equal to -...