Question

H(t)=cot(t) [3pi/2,pi/6] find the average rate of change

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 h(t)=cot(t)\qquad \begin{cases} t_1=(3\pi )/(2)\\ t_2=(\pi )/(6) \end{cases}\implies \cfrac{h\left( (\pi )/(6) \right)-h\left( (3\pi )/(2) \right)}{(\pi )/(6)-(3\pi )/(2)} \\\\\\ \cfrac{cot\left( (\pi )/(6) \right)-cot\left( (3\pi )/(2) \right)}{(\pi )/(6)-(3\pi )/(2)}\implies \cfrac{√(3)-0}{(5\pi )/(3)}\implies \cfrac{3√(3)}{5\pi }`