Second FTC

Let  $g\left(x\right)=\int_1^xt^2+2t-7dt$ . Find  $g'\left(x\right)$  . 

•  $\frac{x^3}{3}+x^2-7x$  

•  $x^2+2x-7$  

•  $2x+2$  

•  $x^2+2x-3$  

Let  $g\left(x\right)=\int_0^xf\left(t\right)dt$ where $f$ is the function whose graph is shown on the left. 

What is the value of  $g\left(0\right)+g\left(2\right)$  ?

• 1.5

• 2.5

• 3.5

• 4.5

Let  $g\left(x\right)=\int_0^xf\left(t\right)dt$ where $f$ is the function whose graph is shown on the left. 

What is the value of  $g'\left(1.897\right)$  ?

• undefined

• 0

• 1

• 2

Consider  $F\left(x\right)=\int_1^{2x}\ \frac{1\ }{1+t^3}dt$ . Find  $F'\left(x\right).$   

•  $\frac{1}{1+8x^2}$  

•  $\frac{1}{1+2x^2}$  

•  $\frac{2}{1+8x^3}-\frac{1}{2}$  

•  $\frac{2}{1+8x^3}$  

The figure shows the graph of a piecewise function  $f$ . For  $-4\le x\le12,$  the function  $g$  is defined by  $g\left(x\right)=\int_0^xf\left(t\right)dt$  . Does  $g$  have a relative minimum, a relative maximum, or neither at  $x=6$ ? Justify your answer.