Math Problem Statement
Bestem tangent for f.docx
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ret min opgave. ret kun fejlene, og lav smiley ved dem der er rigtige
Solution
Here is the corrected solution for your task, along with smiley marks for correct parts:
Given function: Given point:
1. Find :
✅ This part is correct! 😊
2. Find :
First, we need to differentiate : Now, substitute : ❌ This part was incorrect (you had 8 instead of 9).
3. Equation of the tangent line:
Use the formula for the tangent line: Substitute the values: ✅ This part is correct! 😊
So, the corrected solution is:
Would you like further details or have any questions?
Here are 5 related questions for further practice:
- How do you find the derivative of a polynomial function?
- What is the general formula for the tangent line of a function at a point?
- How would you find the normal line to the function at ?
- If the point of tangency is , what would the tangent line equation be?
- What is the significance of the slope of the tangent line in the context of rates of change?
Tip: Always double-check the differentiation process, especially when calculating slopes for tangent lines!
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Tangent Line Calculation
Formulas
f(x) = 2x^3 + 3x
f'(x) = 6x^2 + 3
Tangent Line: y = f'(x_0)(x - x_0) + f(x_0)
Theorems
-
Suitable Grade Level
Grades 10-12
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