How does the graph of g(x)=x+4 compares with the graph of the parent function, f(x)=x?
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a = 11 + 4b - 4c
a = 4b - 4c + 11
a + (-a + 4c) = (4b - 4c + 11) + (-a + 4c)
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Good Luck :)
a = 11 + 4b - 4c
a = 4b - 4c + 11
a + (-a + 4c) = (4b - 4c + 11) + (-a + 4c)
Hope This Helps You!
Good Luck :)
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.