The difference between a number x and 3 is no more than 2
2 answers:
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Questions (contd)
(a) For what amount of driving do the two plans cost the same?
(b) What is the cost when the two plans cost the same?
Answer:
(a) 100 miles
(b) $65
Step-by-step explanation:
Given
Plan 1:
per mile
Plan 2:
per mile
Solving (a): Number of miles when both plans are equal
Represent the distance with x and the cost with y
So:
Plan 1:
Plan 2:
To solve (a), we equate both plans together; i.e.
Collect Like Terms
Solve for x
Hence, 100 mile would cost both plans the same
Solving (b): Cost when both plans are the same:
In this case, we simply substitute 100 for x in any of the y equation.
<em>Hence, the amount is $65</em>
1.) The interval of the value of x is from -5 to 1, inclusive. Remember that what is asked is the absolute value, thus the sign does not matter even if you have to subtract x from 5. Thus, the maximum value would be obtained if the x is smaller, which is 1. The minimum value is obtained when x=-5.
Absolute maximum value: x = - 5
f(-5) = ║5 - 7(-5)^2║ = ║-170║=170
Absolute minimum value: x = 1
f(1) = ║5 - 7(1)^2║ = ║-2║= 2
2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:
The differentiated form would be f'(x) = -2x. Then,
Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.
Absolute maximum value: x = - 5
f(-5) = ║5 - 7(-5)^2║ = ║-170║=170
Absolute minimum value: x = 1
f(1) = ║5 - 7(1)^2║ = ║-2║= 2
2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:
The differentiated form would be f'(x) = -2x. Then,
Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.
