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If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is th

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Question: If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?

Options:

  1. 2
  2. 0
  3. 1
  4. 4

Correct Answer: 2

Solution: 

Calculating P(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.

If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is th

Practice Questions

Q1
If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
  1. 2
  2. 0
  3. 1
  4. 4

Questions & Step-by-Step Solutions

If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
  • Step 1: Identify the polynomial P(x) = x^3 - 3x^2 + 4.
  • Step 2: Substitute x = 1 into the polynomial to find P(1).
  • Step 3: Calculate 1^3, which is 1.
  • Step 4: Calculate 3(1^2), which is 3.
  • Step 5: Now, combine the results: P(1) = 1 - 3 + 4.
  • Step 6: First, do 1 - 3, which equals -2.
  • Step 7: Then, add 4 to -2, which gives you 2.
  • Step 8: Therefore, the value of P(1) is 2.
  • Polynomial Evaluation – The question tests the ability to evaluate a polynomial function at a specific point.
  • Local Maximum – Understanding the concept of local maxima in the context of polynomial functions.
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