Problema Solution
According to data from the National Highway Traffic Safety Administration, the accident rate as a function of the driver in years x can be approximated by the function:
f(x)=0.0232x^2-2.28x+60 for 16(less than or equals)x (less than or equals)85
Find both the age at which the accident rate is a minimum and the minimum rate
Answer provided by our tutors
f(x)=0.0232x^2-2.28x+60 for 16 <= x <=85
we need to find the minimum of the parabolic function f(x)
since the quotient in front of x^2 is 0.0232>0 the function has minimum equal to
f min = c - (b^2)/(4a)
where a = 0.0232, b = -2.28 and c = 60
f min = 60 - (-2.28)^2/(4*0.0232)
f min = 3.98 is minimum accident rate
the minimum rate is 3.98
now we need to find the vertex x
x = - b/(2a)
x = -(-2.28)/(2*0.0232)
x = 49.14 years is the age at which the rate is minimum.