Question

what is the average rate of change of the function ( f(x)=4x^{2}+3x ) on the interval ( 1, ) the average rate of change is

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here \(a = 1\), assume \(b=2\) (since the upper - limit of the interval is cut off, and for a quadratic \(y=4x^{2}+3x\), a common problem would use \(b = 2\) in the absence of other information).

Step2: Calculate \(f(1)\) and \(f(2)\)

• For \(x = 1\):

\(f(1)=4\times(1)^{2}+3\times(1)=4 + 3=7\)

• For \(x = 2\):

\(f(2)=4\times(2)^{2}+3\times(2)=4\times4+6=16 + 6=22\)

Step3: Calculate the average rate of change

\(\frac{f(2)-f(1)}{2 - 1}=\frac{22-7}{1}=15\)

Answer:

\(15\)