Math Problem Statement
Apskaičiuokite funkcijos f(x) išvestinės reikšmę nurodytame taške: f'(-1), kai f(x) = x^3 + x
Solution
The problem asks you to calculate the derivative of the function at .
Step 1: Find the derivative of the function
The derivative of is calculated by applying the power rule:
Using the power rule:
Thus:
Step 2: Evaluate the derivative at
Now, substitute into the derivative:
The derivative at is . However, the answer choices provided are:
- a) -2
- b) -1.5
- c) 2
It seems none of these options match the result . Would you like further clarification or verification on the provided options?
Here are 5 follow-up questions:
- What is the importance of understanding the power rule for differentiation?
- How do higher-order derivatives affect a function's graph?
- Can we apply different methods to calculate derivatives besides the power rule?
- How would the derivative change if the function included more complex terms?
- What does the derivative tell us about the behavior of the function at a given point?
Tip: When solving derivatives, always double-check the power rule's application to avoid simple errors.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Power Rule
Formulas
f'(x) = 3x^2 + 1
Theorems
Power Rule
Suitable Grade Level
High School (Grades 10-12)