Question: For the function f(x) = x^3 - 3x^2 + 4, find the x-coordinate of the point where f is differentiable.
Options:
-1
0
1
2
Correct Answer: 1
Solution:
f(x) is a polynomial and is differentiable everywhere. The x-coordinate can be any real number.
For the function f(x) = x^3 - 3x^2 + 4, find the x-coordinate of the point where
Practice Questions
Q1
For the function f(x) = x^3 - 3x^2 + 4, find the x-coordinate of the point where f is differentiable.
-1
0
1
2
Questions & Step-by-Step Solutions
For the function f(x) = x^3 - 3x^2 + 4, find the x-coordinate of the point where f is differentiable.
Correct Answer: Any real number
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 type of function given. The function f(x) = x^3 - 3x^2 + 4 is a polynomial.
Step 3: Know that polynomials are smooth and continuous everywhere on the real number line.
Step 4: Since f(x) is a polynomial, it is differentiable at every point on the real number line.
Step 5: Conclude that the x-coordinate where f is differentiable can be any real number.
Differentiability of Polynomials – Polynomials are differentiable everywhere on the real number line.
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