Question: Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
Options:
Yes
No
Only at x = 0
Only at x = 2
Correct Answer: Yes
Solution:
This is a polynomial function, which is differentiable everywhere on its domain.
Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
Practice Questions
Q1
Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
Yes
No
Only at x = 0
Only at x = 2
Questions & Step-by-Step Solutions
Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
Step 1: Identify the function given, which is f(x) = x^2 - 4x + 4.
Step 2: Recognize that this function is a polynomial function.
Step 3: Understand that polynomial functions are smooth and continuous.
Step 4: Know that smooth and continuous functions are differentiable everywhere on their domain.
Step 5: Conclude that since f(x) is a polynomial, it is differentiable everywhere.
Differentiability of Polynomial Functions – Polynomial functions are continuous and differentiable everywhere on their domain, which is all real numbers.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
