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The position of moving car at time t is given as f(t) = 3t^2+bt+c, t>0 where a , b,c are real no.>1 Then the avg speed of the car over the time interval [t_1,t_2] is attained at the pt. ....  
Option: 1 \left ( t_2-t_1 \right )/2
Option: 2 a\left ( t_2+t_1 \right )+b
Option: 3 a\left ( t_2+t_1 \right )+b
Option: 4 \left ( t_2+t_1 \right )/2

Answers (1)

best_answer

Using mean value theorem

f'(c)=\frac{f(b)-f(a)}{b-a}

f'(t)=\frac{f(t_2)-f(t_1)}{t_2-t_1}

\\\Rightarrow2 a t+b=\frac{f\left(t_{2}\right)-f\left(t_{1}\right)}{t_{2}-t_{1}} \\\\\Rightarrow 2 a t+b=\frac{a\left(t_{2}^{2}-t_{1}^{2}\right)+b\left(t_{2}-t_{1}\right)}{t_{2}-t_{1}} \\\\ \Rightarrow 2 a t+b=a\left(t_{2}+t_{1}\right)+b \\\\ \Rightarrow \qquad \;\;t=\frac{t_{1}+t_{2}}{2}

 

Correct Answer : Option D

Posted by

himanshu.meshram

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