Let \( f(x)=1+4 x-x^{2} \) and \( g(x)=\left\{\begin{array}{l}\max \{f(t), x \leq t \leq x+1\}, ...

Channel:
Subscribers:
449,000
Published on ● Video Link: https://www.youtube.com/watch?v=9aYqfW-NNg4



Duration: 11:46
1 views
0


Let \( f(x)=1+4 x-x^{2} \) and \( g(x)=\left\{\begin{array}{l}\max \{f(t), x \leq t \leq x+1\}, 0 \leq x3 \\ \min (x+3), \quad 3 \leq x \leq 5\end{array}\right. \) then \( g(x) \) is
(a) Continuous for all \( x \in[0,3] \)
(b) Differentiable for all \( x \in[0,3] \)
(c) Discontinuous at \( x=3 \)
(d) Non-differentiable at \( x=1 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2023-06-08If \( y=(\sin x)^{\left.(\sin x)^{(\sin x)}\right)^{\infty}} \), then \( \frac{d y}{d x}= \) (a)...
2023-06-08Number of points where \( f(x)=[\{x\}+|x+\sin x|] \operatorname{sgn}\left(x^{2}-1\right) \), \( ...
2023-06-08At how many points in the interval \( (0,2): f(x)=x^{2}[2 x]-x\left[x^{2}\right] \) is discontin...
2023-06-08If \( f(x)=\left\{\begin{array}{ll}x \frac{e^{\frac{1}{x}}-e^{\frac{-1}{x}}}{\frac{1}{x} e^{\fra...
2023-06-08(a) An infinite discontinuity (b) Finite discontinuity (c) Oscillatory discontinuity (d) A remov...
2023-06-08Let \( f:(-\infty, \infty) \rightarrow(-\infty, \infty) \) be given by \( f(x)=x|x|+|x-1|- \) \(...
2023-06-08Let \( f(x)=|| e^{x}-1|-1| \) then \( f(x) \) is differentiable at all points except at \( x=0 \...
2023-06-08If \( f(x)=\left\{\begin{array}{cc}\frac{\sin \{\cos x\}}{x-\frac{\pi}{2}} & x \neq \frac{\pi}{2...
2023-06-08If \( f(x)=\left(\frac{x}{2}\right)-1 \), then on the interval \( [0, \pi] \) (a) \( \tan (f(x))...
2023-06-08Let \( f(x)=\operatorname{sgn}(x) \) and \( h(x)=x\left(x^{2}-5 x+6\right) \). The function \( f...
2023-06-08Let \( f(x)=1+4 x-x^{2} \) and \( g(x)=\left\{\begin{array}{l}\max \{f(t), x \leq t \leq x+1\}, ...
2023-06-08The number of points of discontinuity of \( y=f(t) \), where \( f(t)=\frac{3}{2 t^{2}+5 t-3} \) ...
2023-06-08A point \( (x, y) \), where function \( f(x)=[\sin [x]] \) in \( (0,2 \pi) \) is not continuous ...
2023-06-08Let \( f(x)=-1+|x-2| \) and \( g(x)=1-|x| \) then set of all possible value(s) of \( x \) for wh...
2023-06-08If \( y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \), then which of the following is false? (a)...
2023-06-08\( A B C \) is an isosceles triangle inscribed in a circle of radius \( r \). If \( A B=A C \) a...
2023-06-08Let \( \alpha \) be a positive real number. Let \( f: R \rightarrow R \) and \( g:(\alpha, \inft...
2023-06-08Let \( \beta=\lim _{x \rightarrow 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x...
2023-06-08If \( y=\frac{1}{p^{2}+p-2} \) where \( p=\frac{1}{x-1} \), then the number of points of discont...
2023-06-08If \( \beta=\lim _{x \rightarrow 0} \frac{e^{x^{3}}-\left(1-x^{3}\right)^{\frac{1}{3}}+\left(\le...
2023-06-08If \( \lim _{x \rightarrow 0} \frac{\alpha e^{x}+\beta e^{-x}+\gamma \sin x}{x \sin ^{2} x}=\fra...