Question:
The position of a moving car at time $t$ is given by $f(t)=a t^{2}$ $+b t+c, t>0$, where $a, b$ and $c$ are real numbers greater than 1 . Then the average speed of the car over the time interval $\left[t_{1}, t_{2}\right]$ is attained at the point :
Correct Option: , 3
Solution:
Average speed $=f^{\prime}(t)=\frac{f\left(t_{2}\right)-f\left(t_{1}\right)}{t_{2}-t_{1}}$
$2 a t+b=a\left(t_{1}+t_{2}\right)+b \Rightarrow t=\frac{t_{1}+t_{2}}{2}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.