The value of a for which the function $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{{\tan }^{ - 1}}a - 3{x^2},\;0 < x < 1}\\ { - 6x,\;\;x \ge 1} \end{array}} \right.$ has a maximum at $x = 1$, is

JEE MATHEMATICS MCQ: MAXIMA & MINIMA

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Analyzing +4 | -1

The value of a for which the function

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {{{\tan }^{ - 1}}a - 3{x^2},\;0 < x < 1}\\ { - 6x,\;\;x \ge 1} \end{array}} \right.

has a maximum at

x = 1

, is

View answer and explanation

Correct option: D

- 1

Option D (

- 1

) is correct. The function must be continuous and have a non-positive derivative at x=1 for a maximum to occur. This condition is satisfied when a = -1.

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