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If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is th
If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
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If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
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Calculating P(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Questions & Step-by-step Solutions
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Q: If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
Solution:
Calculating P(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Steps: 8
Show Steps
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.
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