Find the t value(s) is the interval (0,8) where the function f(t)=e^(t/6)/t attains its local or absolute minimum value(s). The minimum(s) are t=?

Question

needing help pleaseee

Answer 1

f(t) = (1/t)e^t/6

 

f'(t) = (1/6t)e^t/6- (1/t²)e^t/6

 

0 =  (1/6t)e^t/6- (1/t²)e^t/6

 

0= e^t/6(1/6t - 1/t²)

 

0 = t - 6

 

t = 6

 

When t<6, the slope of the function is negative meaning that the function is decreasing. When t>6, the slope is positive which means the function is increasing. This means the function has a local minimum at t=6