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QJEEM10Maca19: JEE Main 2010 Mathematics - Class 12 JEEM10Maca19 Solution: Let f : R → R be defined by If f has a local minimum at x = − 1 …

Let f:R→R be defined by </mo></mrow><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="ORD"><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>−</mo><mn>2</mn><mi>x</mi><mo>,</mo><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mi>i</mi><mi>f</mi></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mi>x</mi><mo>≤</mo><mo>−</mo><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mi>i</mi><mi>f</mi></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mi>x</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn></mrow></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo></mrow></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>

If fhas a local minimum at x=−1, then a possible value of k is

Multiple Choice Options

  • A 0
  • B −12
  • C −1
  • D 1

Step-by-Step Verified Solution

f(x)={k−2x,ifx≤−12x+3,ifx>−1

AIEEE 2010 Mathematics - Application of Derivatives Question 190 English Explanation

This is true where k=−1

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