Question: If f(x) = x^3 - 4x + 1, what is f\'\'(x)? (2023)
Options:
6x - 4
6x + 4
3x^2 - 4
3x^2 + 4
Correct Answer: 6x - 4
Exam Year: 2023
Solution:
First derivative f\'(x) = 3x^2 - 4, then f\'\'(x) = 6x.
If f(x) = x^3 - 4x + 1, what is f''(x)? (2023)
Practice Questions
Q1
If f(x) = x^3 - 4x + 1, what is f''(x)? (2023)
6x - 4
6x + 4
3x^2 - 4
3x^2 + 4
Questions & Step-by-Step Solutions
If f(x) = x^3 - 4x + 1, what is f''(x)? (2023)
Step 1: Start with the function f(x) = x^3 - 4x + 1.
Step 2: Find the first derivative f'(x) by using the power rule. The derivative of x^3 is 3x^2, and the derivative of -4x is -4. So, f'(x) = 3x^2 - 4.
Step 3: Now, find the second derivative f''(x) by taking the derivative of f'(x). The derivative of 3x^2 is 6x, and the derivative of -4 is 0. So, f''(x) = 6x.
Differentiation – The process of finding the derivative of a function, which measures how the function changes as its input changes.
Second Derivative – The derivative of the first derivative, which provides information about the concavity of the function.
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