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If f(x) = 3x^2 + 2x, what is f'(2)? (2023)
If f(x) = 3x^2 + 2x, what is f'(2)? (2023)
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Practice Questions
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Q1
If f(x) = 3x^2 + 2x, what is f'(2)? (2023)
10
14
12
8
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First, find f'(x) = 6x + 2. Then, f'(2) = 6(2) + 2 = 12 + 2 = 14.
Questions & Step-by-step Solutions
1 item
Q
Q: If f(x) = 3x^2 + 2x, what is f'(2)? (2023)
Solution:
First, find f'(x) = 6x + 2. Then, f'(2) = 6(2) + 2 = 12 + 2 = 14.
Steps: 10
Show Steps
Step 1: Identify the function f(x) = 3x^2 + 2x.
Step 2: Find the derivative of the function, which is f'(x). To do this, use the power rule: the derivative of x^n is n*x^(n-1).
Step 3: Apply the power rule to each term in f(x):
- For 3x^2, the derivative is 2*3x^(2-1) = 6x.
- For 2x, the derivative is 2.
Step 4: Combine the derivatives from Step 3 to get f'(x) = 6x + 2.
Step 5: Now, substitute x = 2 into the derivative f'(x). So, calculate f'(2) = 6(2) + 2.
Step 6: Perform the multiplication: 6(2) = 12.
Step 7: Add 12 and 2 together: 12 + 2 = 14.
Step 8: Therefore, f'(2) = 14.
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