Question

Find the maximum and minimum values , if any of the following functions given by -

i) $f\left(x\right)=lx+2l-1$
ii) $g\left(x\right)=lx+11+3$

iii) $h\left(x\right)=\sin \left(2x\right)+3$
iv) $f\left(x\right)=l\sin 4x+3l$
v) $h\left(x\right)=x+1,x\in (-1,1)$

Answer 1

(i) $f\left(x\right)=lx+2l-1$ (no minima no maxima)

(ii) $g\left(x\right)=lx+11+3$ (no minima no maxima)

(iii) $h\left(x\right)=\sin \left(2x\right)+3$

$-1\le \sin \left(2x\right)\le 1$

$2\le \sin \left(2x\right)+3\le 4$

$\therefore$ minima $=2$ maxima $=4$

(iv) $f\left(x\right)=l\sin \left(4x\right)+3l$ minima $=3l-l$

$=2l$

maxima $=3l+l$

$=4l$

(v) $h\left(x\right)=x+1,x\in (-1,1)$ minima $=-1+1$

$=0$

maxima $=1+1$

$=2$