2. what is the average rate of change of ( g(x)=x^{2} ) on the interval ( 3 leq x leq 9 )?\n(1) 8\n(3)…

2. what is the average rate of change of ( g(x)=x^{2} ) on the interval ( 3 leq x leq 9 )?\n(1) 8\n(3) 15\n(2) 12\n(4) 18\n3. given the graph of the function ( f(x) ) shown below, find the average rate of change over each of the following intervals. express in simplest form. show the calculations you use to find your answers.\n(a) ( -3 leq x leq 1 )\n(b) ( -1 leq x leq 8 )\n(c) ( 1 leq x leq 9 )\n(d) ( -6 leq x leq 2 )\n4. consider the function given by ( f(x)=6 x+5 ). find its average rate of change over the following intervals.\n(a) ( 1 leq x leq 3 )\n(b) ( 2 leq x leq 7 )\n5. the average rate of change should have been the same for both (a) and (b) in the last p what is special about this function that ensures its average rate of change will always be same?

2. what is the average rate of change of ( g(x)=x^{2} ) on the interval ( 3 leq x leq 9 )?\n(1) 8\n(3) 15\n(2) 12\n(4) 18\n3. given the graph of the function ( f(x) ) shown below, find the average rate of change over each of the following intervals. express in simplest form. show the calculations you use to find your answers.\n(a) ( -3 leq x leq 1 )\n(b) ( -1 leq x leq 8 )\n(c) ( 1 leq x leq 9 )\n(d) ( -6 leq x leq 2 )\n4. consider the function given by ( f(x)=6 x+5 ). find its average rate of change over the following intervals.\n(a) ( 1 leq x leq 3 )\n(b) ( 2 leq x leq 7 )\n5. the average rate of change should have been the same for both (a) and (b) in the last p what is special about this function that ensures its average rate of change will always be same?

Answer

Explanation:

Step1: Calcular ( f(3) ) y ( f(1) )

Para ( x = 3 ), ( f(3)=6\times3 + 5=18 + 5=23 ) Para ( x = 1 ), ( f(1)=6\times1+5 = 6 + 5=11 )

Step2: Aplicar la fórmula del promedio

La fórmula del promedio es ( \frac{f(b)-f(a)}{b - a} ), donde ( a = 1 ), ( b = 3 ) ( \frac{f(3)-f(1)}{3 - 1}=\frac{23-11}{2}=\frac{12}{2}=6 )

Step3: Calcular ( f(7) ) y ( f(2) )

Para ( x = 7 ), ( f(7)=6\times7+5=42 + 5 = 47 ) Para ( x = 2 ), ( f(2)=6\times2+5=12 + 5=17 )

Step4: Aplicar la fórmula del promedio

La fórmula del promedio es ( \frac{f(b)-f(a)}{b - a} ), donde ( a = 2 ), ( b = 7 ) ( \frac{f(7)-f(2)}{7 - 2}=\frac{47-17}{5}=\frac{30}{5}=6 )

Answer:

(a) ( 6 ) (b) ( 6 )