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  • Please solve RD Sharma class 12 chapter Maxima and Minima exercise 17.4 question 1 sub question (i) maths textbook solution

Please solve RD Sharma class 12 chapter Maxima and Minima exercise 17.4 question 1 sub question (i) maths textbook solution

Answers (1)

Answer:

        Absolute Maximum = 8 at  x=4,

        Absolute Minimum = -10 at x=-2

Hint:

        Find x where f^{\prime}(x)=0

Given:

        f(x)=4 x-x^{2} / 2 \text { in }[-2,4.5]

Explanation:

        f^{\prime}(x)=4 \times 1-2 x / 2

        \begin{aligned} &=4-x \\ &f^{\prime}(x)=4-x=0 \\ &x=4 \\ &f(4)=4 \times 4-(4)^{2} / 2=16-16 / 2 \end{aligned}

Now, we find the value of f(x) at end points

        \begin{aligned} &f(-2)=4 \times-2-(-2)^{2} / 2=-8-2=-10 \\ &f(4.5)=4 \times 4.5-(4.5)^{2} / 2=18-10.125=7.875 \end{aligned}

Now,

The maximum value of f (x) at x=8 & minimum at x=-2

Hence,

 Absolute maximum = 8 at x=4,

Absolute minimum = -10 at x=-2

Posted by

infoexpert26

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