Mathematics, 26.06.2019 16:30 chubbyxturtle
Determine the value of a so that the average rate of change of f(x)=3x^2+ax-4 over the interval [-1,2] is 8.
Answers: 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{31em}{0.25pt}\\\\ f(x)=3x^2+ax-4 \qquad \begin{cases} x_1=-1\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(-1)}{2-(-1)}~~~~=~~~~8 \\\\\\ \cfrac{[3(2)^2+a(2)-4]~~-~~[3(-1)^2+a(-1)-4]}{2+1}=8 \\\\\\ \cfrac{[12+2a-4]-[3-a-4]}{3}=8\implies \cfrac{2a+8+a+1}{3}=8 \\\\\\ 3a+9=24\implies 3a=15\implies a=\cfrac{15}{3}\implies \boxed{a=5}](/tpl/images/1187/5300/e263a.png)
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Determine the value of a so that the average rate of change of f(x)=3x^2+ax-4 over the interval [-1,...
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