Identify the correct statement about the function given below:
Tap an option to check your answer.
1 mark, −0.33MathematicsLimits, continuity and differentiabilityDifferentiability and its link to continuityModerateabout 2 min
UoH 2021 Question 33: Limits, continuity and differentiability
Answer and worked solution
Checking your account…
Plain-text version
Identify the correct statement about the function given below: f(x) = { x² x ≤ 0; 0 0 < x < 5; (5-x)² x ≥ 5 } (A) The function is continuous as well as differentiable everywhere. (B) The function is neither continuous everywhere nor differentiable everywhere. (C) The function is continuous everywhere but is not differentiable everywhere. (D) The function is not continuous everywhere but is differentiable everywhere.
Also written as: Identify the correct statement about the function given below: f(x) = { x^2 x <= 0; 0 0 < x < 5; (5-x)^2 x >= 5 }
Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.
What this question tests
This question is on Differentiability and its link to continuity, part of Limits, continuity and differentiability in Mathematics.
When a derivative exists and why differentiability implies continuity but not conversely.
TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.
Similar questions from other papers
- Derivative of Average cost (AC) = 5 + 2/Q is
- The value of the first derivative of f(x)=(3x³+2x²+x+1)² evaluated at x=2 is (*in integer*).
- What will be the third derivative of the following rational function? y = g(x) = x/(1+x); (x ≠ -1)
- The exports of goods of a country, G = G(t) has a growth rate of a/t, and its exports of services, S = S(t) has a growth rate of b/t. What is the growth rate of its…
- Let f(x) = -3x²(1-x) - 3x(1-x)² - (1-x)³. Then, df(x)/dx =
Question from the UoH 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.