12.1 Precalc Homework

Question

Find the exact location of all the relative and absolute extrema of the function.

g(t) = e^t − t with domain [−1, 1]

The variable g has a relative maximum at (t,y) =

The variable g has a absolute minimum at (t,y) = (0,1)

The variable g has an absolute maximum at (t,y) =

Answer 1

Hi,

g(t) = e^t − t with domain [−1, 1]

1) find, g'(t) =  e^t − 1

2) g'(t) = 0 ====> e^t − 1 = 0 ====> e^t = 1 =====> t = 0

3) g(0) = 1 ======> ( 0 , 1) is max or min

4) find g(-1 ) and g (1) ====> g(-1 ) = 1/e + 1 AND g (1) = e - 1

5) ( 0 , 1) is abs and local min (1, e-1) is abs max

I hope it is useful,

Minoo