For which value of a is the function f(x) = x^2 - ax + 4 differentiable at x = 2?
Practice Questions
1 question
Q1
For which value of a is the function f(x) = x^2 - ax + 4 differentiable at x = 2?
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f(x) is a polynomial and is differentiable for all a, hence any value of a works.
Questions & Step-by-step Solutions
1 item
Q
Q: For which value of a is the function f(x) = x^2 - ax + 4 differentiable at x = 2?
Solution: f(x) is a polynomial and is differentiable for all a, hence any value of a works.
Steps: 5
Step 1: Understand what it means for a function to be differentiable. A function is differentiable at a point if it has a defined derivative at that point.
Step 2: Identify the function given in the question, which is f(x) = x^2 - ax + 4.
Step 3: Recognize that f(x) is a polynomial function. Polynomial functions are smooth and continuous everywhere.
Step 4: Since f(x) is a polynomial, it is differentiable at all points, including x = 2, regardless of the value of a.
Step 5: Conclude that any value of a will make the function differentiable at x = 2.
