A certain light truck can go around a curve having a radius of $100m$ with a maximum speed of $16\frac{m}{s}$. To have the same acceleration, at what maximum speed (in $\frac{m}{s}$ ) can it go around a curve having a radius of $25m?$

Certainly! Here are the step-by-step solutions for the problem: Given: $f(x)=3x^2-2x+1$ To find: The average rate of change of $f(x)$ over the interval $[1,4]$. Solution: Step 1: Find the value of $f(1)$ and $f(4)$. $f(1)=3(1{)}^2-2(1)+1=2$$f(4)=3(4{)}^2-2(4)+1=41$ Step 2: Use the formula for average rate of change of a function over an interval. The formula for average rate of change of a function $f(x)$ over an interval $[a,b]$ is: $\frac{f(b)-f(a)}{b-a}$ Step 3: Substitute the values found in step 1 into the formula. $\frac{f(4)-f(1)}{4-1}=\frac{41-2}{3}=\frac{39}{3}=13$ Step 4: Simplify the expression. The average rate of change of $f(x)$ over the interval $[1,4]$ is 13. Therefore, the solution is: The average rate of change of $f(x)$ over the interval $[1,4]$ is 13.