Question: What is the slope of the tangent line to the curve y = x^2 - 4x + 5 at x = 3? (2023)
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Correct Answer: 2
Exam Year: 2023
Solution:
The slope is given by f\'(x) = 2x - 4. At x = 3, f\'(3) = 2(3) - 4 = 2.
What is the slope of the tangent line to the curve y = x^2 - 4x + 5 at x = 3? (2
Practice Questions
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What is the slope of the tangent line to the curve y = x^2 - 4x + 5 at x = 3? (2023)
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Questions & Step-by-Step Solutions
What is the slope of the tangent line to the curve y = x^2 - 4x + 5 at x = 3? (2023)
Step 1: Identify the function given in the question, which is y = x^2 - 4x + 5.
Step 2: Find the derivative of the function. The derivative tells us the slope of the tangent line. For y = x^2 - 4x + 5, the derivative is f'(x) = 2x - 4.
Step 3: Substitute x = 3 into the derivative to find the slope at that point. So, calculate f'(3) = 2(3) - 4.
Step 4: Perform the calculation: 2(3) = 6, then 6 - 4 = 2.
Step 5: Conclude that the slope of the tangent line to the curve at x = 3 is 2.
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