Question: The function f(x) = x^2 - 4x + 4 is differentiable everywhere?
Options:
True
False
Only at x = 0
Only at x = 2
Correct Answer: True
Solution:
f(x) is a polynomial function, hence it is differentiable everywhere.
The function f(x) = x^2 - 4x + 4 is differentiable everywhere?
Practice Questions
Q1
The function f(x) = x^2 - 4x + 4 is differentiable everywhere?
True
False
Only at x = 0
Only at x = 2
Questions & Step-by-Step Solutions
The function f(x) = x^2 - 4x + 4 is 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 because it is made up of terms with x raised to whole number powers.
Step 3: Understand that polynomial functions are smooth and continuous everywhere on the real number line.
Step 4: 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.
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