JEE MATHEMATICS MCQ: MAXIMA & MINIMA

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Application +4 | -1

If sum of two numbers is 6, the minimum value of the sum of their reciprocals is

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Correct option: C

\frac{2}{3}

Option C (

\frac{2}{3}

) is correct because it represents the minimum value of the sum of the reciprocals of two numbers whose sum is 6, found using calculus to minimize the function.

More Questions from MAXIMA & MINIMA

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Let

f(x)=\left(1+b^2\right) x^2+2 b x+1

. Let

m(b)

be the minimum value of

f(x)

(that is least value). As

b

varies, the range of

m(b)

is Let

f: R \rightarrow R

be a function defined by

f(x)=(x-3)^{n_1}(x-5)^{n_2}, n_1, n_2 \in N

. Then, which of the following is NOT true? The equation

|2 a x-3|+|a x+1|+|5-a x|=\frac{1}{2}

possesses Let the function

f(x)=2 x^{3}+(2 p-7) x^{2}+3(2 p-9) x

-6 have a maxima for some value of

x<0

and a minima for some value of

x>0

. Then, the set of all values of

p

is The least value of the

f\left( x \right)

given by

f\left( x \right) = {\tan ^{ - 1}}x - \frac{1}{2}{\log _e}x

in the interval

\left[ {1/\sqrt 3 ,\;\sqrt 3 } \right]

, is If the total maximum value of the function

f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0, \frac{\pi}{2}\right),

\frac{k}{e}

, then

\left(\frac{k}{e}\right)^{8}+\frac{k^{8}}{e^{5}}+k^{8}

is equal to