- #1
dnartS
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I'm having a hard time with these two questions for an assignment in grade 12 advanced functions..
1) Find the maximum and minimum values for each exponential growth or decay equation on the given interval.
i) y=100(0.85)t, for 0 (less than or equal to) t (less than or equal to) 5
ii) y = 35(1.15)x, for 0 (less than or equal to) x (lessthan or equal to) 10
(This one has me puzzled, I am not sure where to even start)
and
2) Use an algebraic strategy to verify that the point given for each function is either a maximum or minimum.
i) f(x) = x^3 - 3x ; (-1, 2)
The relevant equation for number 2) would be difference quotient:
f(x) - f(x)+h
h
(h is 0.0001 which is a very close number to 0)so
f(h) = x^3 - 3x
= [(-1)^3 - 3(-1)] - [(-1)^3 - 3(-1) + 0.0001]
0.0001
= 2 - 2.0001
0.0001
= 0
:. The point is a maximum because the slope of the tangent is 0
Now I'm not sure if this is correct, but the answer is supposed to be maximum. Any help would be appreciated because this is really tricky.
1) Find the maximum and minimum values for each exponential growth or decay equation on the given interval.
i) y=100(0.85)t, for 0 (less than or equal to) t (less than or equal to) 5
ii) y = 35(1.15)x, for 0 (less than or equal to) x (lessthan or equal to) 10
(This one has me puzzled, I am not sure where to even start)
and
2) Use an algebraic strategy to verify that the point given for each function is either a maximum or minimum.
i) f(x) = x^3 - 3x ; (-1, 2)
The relevant equation for number 2) would be difference quotient:
f(x) - f(x)+h
h
(h is 0.0001 which is a very close number to 0)so
f(h) = x^3 - 3x
= [(-1)^3 - 3(-1)] - [(-1)^3 - 3(-1) + 0.0001]
0.0001
= 2 - 2.0001
0.0001
= 0
:. The point is a maximum because the slope of the tangent is 0
Now I'm not sure if this is correct, but the answer is supposed to be maximum. Any help would be appreciated because this is really tricky.