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UPCET / UPSEE System from Extrema — practice questions

Explore 1 free System from Extrema questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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System from Extrema questions and exercises with answers

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If $y = a \ln x + b x^2 + x$ has extreme values at $x = 1$ and $x = 2$, then $(a, b)$ is:Read the answer and worked solution →

Worked practice questions

If $y = a \ln x + b x^2 + x$ has extreme values at $x = 1$ and $x = 2$, then $(a, b)$ is:

  1. $(-2/3, -1/6)$
  2. $(2, 1)$
  3. $(-1, 1)$
  4. $(2/3, 1/6)$
Show answer and solution

Correct answer: A. $(-2/3, -1/6)$

$y' = a/x + 2bx + 1 = 0$. At $x = 1$: $a + 2b + 1 = 0$. At $x = 2$: $a/2 + 4b + 1 = 0$. **Solving:** from first, $a = -2b - 1$. **Sub into second:** $(-2b - 1)/2 + 4b + 1 = 0$ ⇒ $-b - 0.5 + 4b + 1 = 0$ ⇒ $3b = -0.5$ ⇒ $b = -1/6$. Then $a = -2(-1/6) - 1 = 1/3 - 1 = -2/3$.

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