has critical points where the derivative is 0:
the second derivative is
and , which indicates a local minimum at with a value of .
at the endpoints of [-2, 2], we have and , so that has an absolute minimum of and an absolute maximum of on [-2, 2].
so we have
all you have to do here is create a few equations to you out. we'll use the variables a, b, and c to match their first initials.
if anne is twice as old as bill, then you can say bill's age must equal 2a (double anne's age). so, we have b = 2a. next, bill is 3 years older than christie, so translating that into math symbols, we can say b = 3 + c. lastly, anne and christie's ages equal 72, so a + c = 72. let's line those up:
b = 2a
b = 3 + c
a + c = 72
since you have two equations that say b = you can combine those into one. if b equals both 2a and 3 + c, then those two values must equal each other:
equation 1: 3 + c = 2a
equation 2: a + c = 72
from here, you can solve this any way you want. the easiest way is to solve for one variable and plug it into the other:
3 + c = 2a add 3 to both sides
c = 3 + 2a now plug this into the second equation
a + (3 + 2a) = 72
now we only have one variable to deal with, so you can get anne's age pretty easily. simplify.
3a + 3 = 72
3a = 69
a = 23
now you have anne's age, so go back to either equation 1 or equation 2 above and plug in your a-value.
23 + c = 72
c = 49
and lastly, we want to find bill's age. read the problem again, and see that bill is 3 years older than christie. this makes bill 52, but we don't need that for the final answer. to find anne and christie's age difference, all you do is take 49 - 23 = 26. they are 26 years apart.
d. substitution property; prove