LMN ~ TSP Find the value of x.
1 answer:
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Answer:
Minimum : -37 at x=2.4 and
Maximum = 37 at x=-2.4.
Step-by-step explanation:
Given:
; [-3,3]
Explanation:
In order to find minimum/maximum of a function, we need to find the first derivative of the function and then set it equal to 0 to get critical points.
Therefore,
Setting derivative equal to 0, we get
On applying quadratic formula, we get
x=2.4, -2.4, -0.7, 0.7.
So, those are critical points of the given function.
Plugging the values x=2.4, -2.4, -0.7, 0.7, -3 and 3 in above function, we get
f(2.4)=(2.4)^5-10(2.4)^3+9(2.4)= -37.01376 : Minimum.
f(-2.4)=(-2.4)^5-10(-2.4)^3+9(-2.4)= 37.01376 : Maximum.
f(0.7)=(0.7)^5-10(0.7)^3+9(0.7) = 3.03807
f(-0.7)=(-0.7)^5-10(-0.7)^3+9(-0.7) = -3.03807
f(-3)=(-3)^5-10(-3)^3+9(-3) =0
f(3)=(3)^5-10(3)^3+9(3) =0
Therefore the approximate values of the minimum and maximum points of f(x) = on [-3,3] are:
Minimum : -37 at x=2.4 and
Maximum = 37 at x=-2.4.
Answer:
a) where "
" stands for the number of miles driven.
b) He can drive as far as 250 miles to keep the rental cost limited to $140.
Step-by-step explanation:
a) Robert wants to make sure that the addition of the costs coming from the car rental per week ($91) plus the amount paid for the coverage of "x" number of miles (which goes as $0.14 times x) does not exceed $140 (which is the same as saying that this total cost must be smaller than or equal to $140.
In math terms, such is written as:
where "x" stands for the number of miles driven.
b) the total number of miles (x) he is allowed to cover given the $140 restriction is obtained by solving for "x" (the number of driven miles) in the inequality of part a):
which tells us that the number of driven miles (x) has to be smaller or equal to 350 miles. Then he can drive as far as 250 miles to keep the rental cost limited to $140.