Question

What is the rate of change for f(x) =7 sin x-1 on the interval from x=0 to x=piover 2

Answer 1

`\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------`


`\bf f(x)= 7sin(x)-1 \qquad \begin{cases} x_1=0\\ x_2=(\pi )/(2) \end{cases}\implies \cfrac{f\left( (\pi )/(2) \right)-f(0)}{(\pi )/(2)-0} \\\\\\ \cfrac{[7\cdot 1-1]~-~[7\cdot 0-1]}{(\pi )/(2)}\implies \cfrac{6-(-1)}{(\pi )/(2)}\implies \cfrac{6+1}{(\pi )/(2)}\implies \cfrac{7}{(\pi )/(2)}\implies \cfrac{14}{\pi }`