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Answer :
To calculate f'(x) for the function f(x) = 2x^3 - 4x^2 + 6x - 25, apply the power rule to obtain f'(x) = 6x^2 - 8x + 6, so the correct answer is B) 6x^2 - 8x + 6.
To find the derivative f'(x) for the function f(x) = 2x3 - 4x2 + 6x - 25, we'll apply the power rule for derivatives. The power rule states that the derivative of xn is nxn-1.
Using the power rule on each term:
- The derivative of 2x3 is 6x2.
- The derivative of -4x2 is -8x.
- The derivative of 6x is 6.
- The derivative of any constant, such as -25, is 0.
Combining these results, the derivative f'(x) is:
f'(x) = 6x2 - 8x + 6
Therefore, the correct answer is B) 6x2 - 8x + 6.
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