If \( f(x) \) is a cubic polynomial which has local maximum at \( x=-1 \). If \( f(2)=18, f(1)=-... VIDEO
If \( f(x) \) is a cubic polynomial which has local maximum at \( x=-1 \). If \( f(2)=18, f(1)=-1 \) and \( f^{\prime}(x) \) has local minimum at \( x=0 \), then [More than One Correct Option, 2006]
(a) the distance between \( (-1,2) \) and \( (a, f(a)) \), where \( x=a \) is the point of local minima, is \( 2 \sqrt{5} \)
(b) \( f(x) \) is increasing for \( x \in[1,2 \sqrt{5}] \)
(c) \( f(x) \) has local minima at \( x=1 \)
(d) the value of \( f(0)=5 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2022-10-27 Statement I \( \frac{5}{3} \) and \( \frac{5}{4} \) are the eccentricities of two conjugate hype... 2022-10-27 If unit vectors \( a \) and \( b \) are inclined at an angle \( 2 \theta \) such that \( |\mathb... 2022-10-27 Statement I In an ellipse the distance between foci is always less than the sum of focal distanc... 2022-10-27 The line which contains all points \( (x, y, z) \) which are of the form \( (x, y, z)=(2,-2,5)+\... 2022-10-27 Statement I Tangents cannot be drawn from the point \( (1, \lambda) \) to the circle \( x^{2}+y^... 2022-10-27 If \( \mathbf{p}, \mathbf{q} \) are two non-collinear vectors such that \( (b-c) \mathbf{p} \tim... 2022-10-27 Let \( f: R \rightarrow R \) be defined as \( f(x)=|x|+\left|x^{2}-1\right| \). Total number of ... 2022-10-27 The value of \( x \) for which the angle between the vectors \( \mathbf{a}=-3 \hat{\mathbf{i}}+x... 2022-10-27 If the volume of a parallelopiped whose adjacent edges are \( \mathbf{a}=2 \hat{\mathbf{i}}+3 \h... 2022-10-27 On the \( x y \) plane where \( O \) is the origin, given points, \( A(1,0), B(0,1) \) and \( C(... 2022-10-27 If \( f(x) \) is a cubic polynomial which has local maximum at \( x=-1 \). If \( f(2)=18, f(1)=-... 2022-10-27 Let \( f \) be a function defined on \( R \) (the set of all real numbers) such that \( f^{\prim... 2022-10-27 A wire of length 2 units is cut into two parts which are bent respectively to form a square of s... 2022-10-27 The maximum value of the function \( f(x)=2 x^{3}-15 x^{2}+36 x-48 \) on the set
\( A=\left\{x \... 2022-10-27 Which of the following is true?
[Passage Based Question, 2008]
(a) \( f(x) \) is decreasing on \... 2022-10-27 Find a point on the curve \( x^{2}+2 y^{2}=6 \) whose distance from the line \( x+y=7 \), is min... 2022-10-27 If \( x=-1 \) and \( x=2 \) are extreme points of \( f(x)=\alpha \log |x|+\beta x^{2}+x \), then... 2022-10-27 Let \( p(x) \) be a real polynomial of least degree which has a local maximum at \( x=1 \) and a... 2022-10-27 The maximum value of the expression \( \frac{1}{\sin ^{2} \theta+3 \sin \theta \cos \theta+5 \co... 2022-10-27 If \( f(x)=\left\{\begin{array}{cl}e^{x}, & 0 \leq x \leq 1 \\ 2-e^{x-1}, & 1x \leq 2 \\ x-e, & ... 2022-10-27 Consider the function \( f:(-\infty, \infty) \rightarrow(-\infty, \infty) \) defined by \( f(x)=...