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What is the derivative of f(x) = x^3 - 4x^2 + 6x?

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Question: What is the derivative of f(x) = x^3 - 4x^2 + 6x?

Options:

  1. 3x^2 - 8x + 6
  2. 3x^2 + 8x + 6
  3. 2x^2 - 4x + 6
  4. 3x^2 - 4x + 6

Correct Answer: 3x^2 - 8x + 6

Solution: 

The derivative f\'(x) = d/dx(x^3 - 4x^2 + 6x) = 3x^2 - 8x + 6.

What is the derivative of f(x) = x^3 - 4x^2 + 6x?

Practice Questions

Q1
What is the derivative of f(x) = x^3 - 4x^2 + 6x?
  1. 3x^2 - 8x + 6
  2. 3x^2 + 8x + 6
  3. 2x^2 - 4x + 6
  4. 3x^2 - 4x + 6

Questions & Step-by-Step Solutions

What is the derivative of f(x) = x^3 - 4x^2 + 6x?
Correct Answer: 3x^2 - 8x + 6
  • Step 1: Identify the function you want to differentiate. In this case, it is f(x) = x^3 - 4x^2 + 6x.
  • Step 2: Recall the power rule for differentiation. The power rule states that if you have x^n, the derivative is n*x^(n-1).
  • Step 3: Apply the power rule to each term in the function f(x).
  • Step 4: Differentiate the first term, x^3. Using the power rule, the derivative is 3*x^(3-1) = 3x^2.
  • Step 5: Differentiate the second term, -4x^2. Using the power rule, the derivative is -4*2*x^(2-1) = -8x.
  • Step 6: Differentiate the third term, 6x. The derivative of x is 1, so the derivative is 6*1 = 6.
  • Step 7: Combine all the derivatives from the previous steps. You get f'(x) = 3x^2 - 8x + 6.
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