AP Calculus ABeasymcq1 pt
If f(x) = 3x⁴ - 2x³ + 5x - 7, then f'(x) = ?
A.12x³ - 6x² + 5
B.12x³ - 6x² + 5x
C.12x³ - 6x² - 5
D.3x³ - 2x² + 5
Explanation
Core Concept
Using the power rule for differentiation, we bring down the exponent and multiply it by the coefficient, then reduce the exponent by 1 for each term. For 3x⁴, we get 12x³. For -2x³, we get -6x². For 5x, we get 5. The derivative of a constant (-7) is 0. So f'(x) = 12x³ - 6x² + 5, which is option A. Option B is incorrect because it has an extra x in the last term. Option C is incorrect because it has a negative sign for the last term. Option D is incorrect because it doesn't apply the power rule correctly.
Correct Answer
A12x³ - 6x² + 5
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