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1 answer:
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Answer:
There are 26 purple marbles in the bag.
Step-by-step explanation:
Firstly, you have to make an expression in terms of x where x represent red marbles. Given that the question says purple marbles is 2 more than 3 times the number of red marbles. So the expression is :
Let red marbles = x,
Next, given that the total marbles in the bag is 34 so you have to add both marbles together and solve the value of x :
Lastly, you have to substitute the value of x into the expression of purple marbles :
Let x = 8,
Answer:
N(1)=50 is a minimum
N(15)=4391.7 is a maximum
Step-by-step explanation:
<u>Extrema values of functions </u>
If the first and second derivative of a function f exists, then f'(a)=0 will produce values for a called critical points. If a is a critical point and f''(a) is negative, then x=a is a local maximum, if f''(a) is positive, then x=a is a local minimum.
We are given a function (corrected)
(a)
First, we take its derivative
Solve N'(t)=0
Simplifying
Solving for t
Only t=1 belongs to the valid interval
Taking the second derivative
Which is always positive, so t=1 is a minimum
(b)
N(1)=50 is a minimum
(c) Since no local maximum can be found, we test for the endpoints. t=1 was already determined as a minimum, we take t=15
(d)
N(15)=4391.7 is a maximum