MATH218 TEST 2

Determine the critical points for the following function: $p\left(w\right)=w^3-4w^2-7w-1$  

•  $x\ =\ 1\ \&\ x=7$  

•  $x=-1\ \&\ x=\frac{7}{3}$  

•  $w=-1\ \&\ w=\frac{7}{3}$  

•  $x=1\ \&\ x=3$  

Determine the critical points of the function: $R\left(x\right)=8x^3-18x^2-240x+2$  

•  $x=4\ \&\ x=\frac{-10}{4}$  

•  $x=4\ \&\ x=\frac{5}{2}$  

•  $x\ =\ 4\ \&\ x=40$  

•  $x=1\ \&\ x\ =\ 7$  

Evaluate the given integral: $\int_{ }^{ }3x^4-\frac{2}{x^2}+\frac{1}{x}dx$  

•  $\frac{3x^5}{5}+\frac{4}{x}+\ln\left|x\right|+c$  

•  $\frac{3x^5}{5}+\frac{2}{x}+\ln\left|x\right|+c$  

•  $\frac{x^5}{5}+\frac{2}{x}-\ln\left|x\right|+c$  

•  $\frac{3x^5}{5}+\frac{2}{x^3}+\ln\left|x\right|+c$  

Evaluate the given integral: $\int_{ }^{ }\frac{\left(1-x\right)\left(2+x\right)}{x}dx$  

•  $2\ln\left|x\right|-x-\frac{x^2}{2}$  

•  $2\ln\left|x\right|+x+\frac{x^2}{2}+c$  

•  $2\ln\left|x\right|-x-\frac{x^2}{2}+c$  

•  $\ln\left|x\right|-2x+\frac{x^2}{2}+c$  

Evaluate the given integral: $\int_{ }^{ }\left(2-t^2\right)e^{\left(6t-t^3\right)}dt$  

•  $\frac{e^{\left(6t-t^3\right)}}{6}+c$  

•  $e^{\left(6t-t^3\right)}+c$  

•  $e^{\left(t-3t^2\right)}+c$  

•  $e^{\left(6t-t^3\right)}$  

Evaluate the given integral: $\int_{ }^{ }\frac{\left(\ln\left(w^2\right)\right)^4}{w}dw$  

•  $\frac{1}{10}\left(\ln\left(w^2\right)\right)^5+c$  

•  $\frac{1}{2}\left(\ln\left(w^2\right)\right)^5+c$  

•  $\frac{2}{10}\left(\ln\left(w^2\right)\right)^5+c$  

•  $\frac{2}{10}\left(\ln\left(w^2\right)\right)^5$  

Evaluate the given integral: $\int_0^6\left|10-2z\right|\ dz$  

• 24

• 25

• 27

• 26

Evaluate the given integral: $\int_0^1\frac{w^3}{6w^4+3}dw$  

• 0.5

•  $\ln\left(3\right)+c$  
  

•  $\frac{1}{24}\ln\left(3\right)$  
  

•  $\frac{1}{24}$  
  

Determine f(x) given that $f'\left(x\right)=12x^5+30x^2$  and f(4)= -23.

•  $f\left(x\right)=2x^6+10x^3-8855$  

•  $f\left(x\right)=2x^6+10x^3+8855$  

•  $f\left(x\right)=2x^6+10x^3+c$  

•  $f\left(x\right)=x^6+x^3+8855$