Let \( a b \in R \) be such that the function \( f \) given by \( f(x)=\log |x|+b x^{2}+a x, x \... VIDEO
Let \( a b \in R \) be such that the function \( f \) given by \( f(x)=\log |x|+b x^{2}+a x, x \neq 0 \) has extreme values at \( x=-1 \) and \( x=2 \)
Statement \( \mathrm{I} f \) has local maximum at \( x=-1 \) and at \( x=2 \) Statement II \( a=\frac{1}{2} \) and \( b=\frac{-1}{4} \)
[2012 AJEEE]
(a) Statement I is false, Statement II is true
(b) Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I
(c) Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I
(d) Statement I is true, Statement \( I I \) is false
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2022-10-27 What is the \( \mathrm{pH} \) of a neutral solution at \( 37^{\circ} \mathrm{C} \), where \( K_{... 2022-10-27 The \( \mathrm{pH} \) of an aqueous solution of sodium chloride at \( 60^{\circ} \mathrm{C} \) i... 2022-10-27 When rain is accompanied by a thunderstorm, the collected rain water will have a \( \mathrm{pH} ... 2022-10-27 The degree of dissociation of pure water at \( 25^{\circ} \mathrm{C} \) is found to be \( 1.8 \t... 2022-10-27 The \( \mathrm{pH} \) of water is \( 7.0 \) at \( 25^{\circ} \mathrm{C} \). If water is heated t... 2022-10-27 A vector equally inclined to the vectors \( \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}} \... 2022-10-27 Let \( a \) and \( b \) be two non-collinear unit vectors. If \( \mathbf{u}=\mathbf{a}-(\mathbf{... 2022-10-27 For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) def... 2022-10-27 Which of the following molecules will have different values of standard molar enthalpy of format... 2022-10-27 The heat of combustion of glycogen is about 432 \( \mathrm{kJ} / \mathrm{mol} \) of carbon. Assu... 2022-10-27 Let \( a b \in R \) be such that the function \( f \) given by \( f(x)=\log |x|+b x^{2}+a x, x \... 2022-10-27 The oxidation state of bismuth in lithium bismuthate is
(a) \( +5 \)
(b) \( +3 \)
(c) \( +2 \)
(... 2022-10-27 The vectors \( \mathbf{a}, \mathbf{b} \) and \( \mathbf{a}+\mathbf{b} \) are
(a) collinear
(b) c... 2022-10-27 Value of \( \lambda \) do the planes \( x-y+z+1=0 \), \( \lambda x+3 y+2 z-3=0,3 x+\lambda y+z-2... 2022-10-27 A point \( P \) moves on the plane \( \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 \) which is fixed. T... 2022-10-27 The distance of the point \( P(-2,3,-4) \) from the line \( \frac{x+2}{3}=\frac{2 y+3}{4}=\frac{... 2022-10-27 If the lattice point \( P(x, y, z), x, y, z0 \) and \( x, y, z \in I \) with least value of \( z... 2022-10-27 The position vectors of the four angular points of a tetrahedron \( O A B C \) are \( (0,0,0),(0... 2022-10-27 For the circle \( x^{2}+y^{2}=r^{2} \), find the value of \( r \) for which the area enclosed by... 2022-10-27 The points \( A(4,5,10), B(2,3,4) \) and \( C(1,2,-1) \) are three vertices of a parallelogram \... 2022-10-27 If the line \( \frac{x}{1}=\frac{y}{2}=\frac{z}{3} \) intersects the line \( 3 \beta^{2} x+3(1-2...