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JEE MATHEMATICS MCQ: MAXIMA & MINIMA

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Analyzing +4 | -1
The denominator of a fraction is greatest then 16 of the square of numerator, then least value of fraction is
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Correct option: B
βˆ’18\frac{{ - 1}}{8}
Option B (βˆ’18\frac{{ - 1}}{8}) is correct because it represents the minimum value of the fraction, found by analyzing its derivative and critical points.

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Let f(x)=(1+b2)x2+2bx+1f(x)=\left(1+b^2\right) x^2+2 b x+1. Let m(b)m(b) be the minimum value of f(x)f(x) (that is least value). As bb varies, the range of m(b)m(b) is Let f:Rβ†’Rf: R \rightarrow R be a function defined by f(x)=(xβˆ’3)n1(xβˆ’5)n2,n1,n2∈Nf(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 ∣2axβˆ’3∣+∣ax+1∣+∣5βˆ’ax∣=12|2 a x-3|+|a x+1|+|5-a x|=\frac{1}{2} possesses Let the function f(x)=2x3+(2pβˆ’7)x2+3(2pβˆ’9)xf(x)=2 x^{3}+(2 p-7) x^{2}+3(2 p-9) x -6 have a maxima for some value of x<0x<0 and a minima for some value of x>0x>0. Then, the set of all values of pp is The least value of the f(x)f\left( x \right) given by f(x)=tanβ‘βˆ’1xβˆ’12log⁑exf\left( x \right) = {\tan ^{ - 1}}x - \frac{1}{2}{\log _e}x in the interval [1/3,β€…β€Š3]\left[ {1/\sqrt 3 ,\;\sqrt 3 } \right], is If the total maximum value of the function f(x)=(3e2sin⁑x)sin⁑2x,x∈(0,Ο€2),f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0, \frac{\pi}{2}\right), is ke\frac{k}{e}, then (ke)8+k8e5+k8\left(\frac{k}{e}\right)^{8}+\frac{k^{8}}{e^{5}}+k^{8} is equal to
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