JEE MATHEMATICS MCQ: MAXIMA & MINIMA

1 Hard

1 of 1

Analyzing +4 | -1

A population

p\left( t \right)

of 1000 bacteria introduced into nutrient medium grows according to the relation

p\left( t \right) = 1000 + \frac{{1000t}}{{100 + {t^2}}}

. The maximum size of this bacterial population is

View answer and explanation

Correct option: C

1050

Option C (1050) is correct because it represents the maximum size of the bacterial population, found by analyzing the derivative of the population function.

More Questions from MAXIMA & MINIMA

Practice All Chapter MCQs →

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