Question

Find the average rate of change of the function f(x) equals -1X^2-4x-3 from x=-1 to x=5

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}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=-x^2-4x-3 \qquad \begin{cases} x_1=-1\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(-1)}{5-(-1)} \\\\\\ \cfrac{[-(5)^2-4(5)-3]~~-~~[-(-1)^2-4(-1)-3]}{5+1} \\\\\\ \cfrac{[-25-20-3]-[-1+4-3]}{6}\implies \cfrac{[-48]-[0]}{6}\implies \cfrac{-48}{6}\implies -8`