The position of a moving car at time t is
given by f(t) = at2 + bt + 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 [t1
, t2
] is
attained at the point :
Solution
V<sub>av</sub> = ${{f\left( {{t_2}} \right) - f\left( {{t_1}} \right)} \over {{t_2} - {t_1}}}$ = f'(t)
<br><br>$\Rightarrow$ $${{a\left( {t_2^2 - t_1^2} \right) - b\left( {{t_2} - {t_1}} \right)} \over {{t_2} - {t_1}}}$$ = 2$a$t + b
<br><br>$\Rightarrow$ a(t<sub>2</sub> + t<sub>1</sub>) + b = 2at + b
<br><br>$\Rightarrow$ t = ${{{t_1} + {t_2}} \over 2}$
About this question
Subject: Mathematics · Chapter: Application of Derivatives · Topic: Tangents and Normals
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