If \( f(x)=\left\{\begin{array}{cl}e^{x}, & 0 \leq x \leq 1 \\ 2-e^{x-1}, & 1x \leq 2 \\ x-e, & ...

Channel:
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=OktLhseWwnw



Duration: 3:19
1 views
0


If \( f(x)=\left\{\begin{array}{cl}e^{x}, & 0 \leq x \leq 1 \\ 2-e^{x-1}, & 1x \leq 2 \\ x-e, & 2x \leq 3\end{array}\right. \) and \( g(x)=\int_{0}^{x} f(t) d t \)
\( x \in[1,3] \) then \( \quad \) [More than One Correct Option, 2006]
(a) \( g(x) \) has local maxima at \( x=1+\log _{e} 2 \) and local minima at \( x=e \)
(b) \( f(x) \) has local maxima at \( x=1 \) and local minima at \( x=2 \)
(c) \( g(x) \) has no local minima
(d) \( f(x) \) has no local maxima
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2022-10-27On the \( x y \) plane where \( O \) is the origin, given points, \( A(1,0), B(0,1) \) and \( C(...
2022-10-27If unit vectors \( a \) and \( b \) are inclined at an angle \( 2 \theta \) such that \( |\mathb...
2022-10-27The value of \( x \) for which the angle between the vectors \( \mathbf{a}=-3 \hat{\mathbf{i}}+x...
2022-10-27If the volume of a parallelopiped whose adjacent edges are \( \mathbf{a}=2 \hat{\mathbf{i}}+3 \h...
2022-10-27A wire of length 2 units is cut into two parts which are bent respectively to form a square of s...
2022-10-27If \( x=-1 \) and \( x=2 \) are extreme points of \( f(x)=\alpha \log |x|+\beta x^{2}+x \), then...
2022-10-27The maximum value of the function \( f(x)=2 x^{3}-15 x^{2}+36 x-48 \) on the set \( A=\left\{x \...
2022-10-27Let \( f: R \rightarrow R \) be defined as \( f(x)=|x|+\left|x^{2}-1\right| \). Total number of ...
2022-10-27The maximum value of the expression \( \frac{1}{\sin ^{2} \theta+3 \sin \theta \cos \theta+5 \co...
2022-10-27Let \( f \) be a function defined on \( R \) (the set of all real numbers) such that \( f^{\prim...
2022-10-27If \( f(x)=\left\{\begin{array}{cl}e^{x}, & 0 \leq x \leq 1 \\ 2-e^{x-1}, & 1x \leq 2 \\ x-e, & ...
2022-10-27If \( f(x) \) is a cubic polynomial which has local maximum at \( x=-1 \). If \( f(2)=18, f(1)=-...
2022-10-27Find a point on the curve \( x^{2}+2 y^{2}=6 \) whose distance from the line \( x+y=7 \), is min...
2022-10-27Consider the function \( f:(-\infty, \infty) \rightarrow(-\infty, \infty) \) defined by \( f(x)=...
2022-10-27Which of the following is true? [Passage Based Question, 2008] (a) \( f(x) \) is decreasing on \...
2022-10-27If \( f(x)=x^{2}+2 b x+2 c^{2} \) and \( g(x)=-x^{2}-2 c x+b^{2} \), such that \( \min f(x)\max ...
2022-10-27The maximum value of \( \left(\cos \alpha_{1}\right) \cdot\left(\cos \alpha_{2}\right) \cdot \ld...
2022-10-27The total number of local maxima and local minima of the function \( f(x)=\left\{\begin{array}{l...
2022-10-27The second degree polynomial \( f(x) \), satisfying \( f(0)=0 \), \( f(1)=1, f^{\prime}(x)0 \for...
2022-10-27A rectangular sheet of fixed perimeter with sides having their lengths in the ratio \( 8: 15 \) ...
2022-10-27Let \( f, g \) and \( h \) be real-valued functions defined on the interval \( [0,1] \) by \( f(...



Tags:
pw