4.3 Maxima and minima  (Page 6/15)

Absolute maximum at $x=2$ and absolute minima at $x=\text{±}3$

Absolute minimum at $x=1$ and absolute maximum at $x=2$

Absolute maximum at $x=4,$ absolute minimum at $x=\mathrm{-1},$ local maximum at $x=\mathrm{-2},$ and a critical point that is not a maximum or minimum at $x=2$

Absolute maxima at $x=2$ and $x=\mathrm{-3},$ local minimum at $x=1,$ and absolute minimum at $x=4$

$y=4x^3-3x$

$y=4\sqrt{x}-x^2$

$y=\frac{1}{x-1}$

$y=\text{ln}(x-2)$

$y=\text{tan}(x)$

$y=\sqrt{4-x^2}$

$y=x^{3\text{/}2}-3x^{5\text{/}2}$

$y=\frac{x^2-1}{x^2+2x-3}$

$y={\text{sin}}^2(x)$

$y=x+\frac{1}{x}$

$f(x)=x^2+3$ over $[\mathrm{-1},4]$

$y=x^2+\frac{2}{x}$ over $[1,4]$

$y={\left(x-x^2\right)}^2$ over $[\mathrm{-1},1]$

$y=\frac{1}{\left(x-x^2\right)}$ over $[0,1]$

$y=\sqrt{9-x}$ over $[1,9]$

$y=x+\text{sin}(x)$ over $[0,2\pi ]$

$y=\frac{x}{1+x}$ over $[0,100]$

$y=\left|x+1\right|+\left|x-1\right|$ over $[\mathrm{-3},2]$

$y=\sqrt{x}-\sqrt{x^3}$ over $[0,4]$

$y=\text{sin}x+\text{cos}x$ over $[0,2\pi ]$

$y=4\text{sin}\theta -3\text{cos}\theta$ over $[0,2\pi ]$

$y=x^2+4x+5$

$y=x^3-12x$

$y=3x^4+8x^3-18x^2$

$y=x^3{\left(1-x\right)}^6$

$y=\frac{x^2+x+6}{x-1}$

$y=\frac{x^2-1}{x-1}$

[T] $y=3x\sqrt{1-x^2}$

[T] $y=x+\text{sin}(x)$

[T] $y=12x^5+45x^4+20x^3-90x^2-120x+3$

[T] $y=\frac{x^3+6x^2-x-30}{x-2}$

[T] $y=\frac{\sqrt{4-x^2}}{\sqrt{4+x^2}}$

A company that produces cell phones has a cost function of $C=x^2-1200x+\mathrm{36,400},$ where $C$ is cost in dollars and $x$ is number of cell phones produced (in thousands). How many units of cell phone (in thousands) minimizes this cost function?

A ball is thrown into the air and its position is given by $h\left(t\right)=\mathrm{-4.9}{t}^2+60t+5\text{m}.$ Find the height at which the ball stops ascending. How long after it is thrown does this happen?

Find when the maximum (local and global) gold production occurred, and the amount of gold produced during that maximum.

Find when the minimum (local and global) gold production occurred. What was the amount of gold produced during this minimum?

$y=\{\begin{array}{cc}{x}^2-4x& 0\le x\le 1\\ x^2-4& 1<x\le 2\end{array}$

$y=\{\begin{array}{cc}{x}^2+1& x\le 1\\ x^2-4x+5& x>1\end{array}$

$y=a{x}^2+bx+c,$ given that $a>0$

$y={\left(x-1\right)}^a,$ given that $a>1$