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

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

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