1. Consider the function f(x) = (3x+5)/(6x+2). For this function there are two important intervals: (negative infinity, A) and (A, positive infinity) where the function is not defined at A.
Find A _________
2. For x E [-15, 13] the function f is defined by: f(x) = x^7 (x+4)^2
On which two intervals is the function increasing? _____ to ______ and ______ to _______
Find the region in which the function is positive: ____ to _____
Where does the function achieve its minimum?
Thank you so much for ANY help! :)
Find A _________
2. For x E [-15, 13] the function f is defined by: f(x) = x^7 (x+4)^2
On which two intervals is the function increasing? _____ to ______ and ______ to _______
Find the region in which the function is positive: ____ to _____
Where does the function achieve its minimum?
Thank you so much for ANY help! :)
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Function is not defined when denominator equals zero:
6x + 2 = 0
6x = -2
x = -2/6 = -1/3 = A
=======================================…
f(x) = x^7 * (x+4)^2
f '(x) = 7x^6*(x+4)^2 + x^7 * 2(x+4)*1
f '(x) = (x+4)*(2x^7 + 7x^6(x+4))
f '(x) = (x+4)*(9x^7 + 28x^6)
f '(x) = x^6 * (x+4) * (9x+28)
On [-15, 13]
f(x) = x^7 * (x+4)^2 equals zero at x = 0, -4
f(-5) = (-5)^7 * (-5+4)^2 a negative number times a positive one, therefor negative
f(-3) = (-3)^7 * (-3+4)^2 a negative number times a positive one, therefor negative
f(1) = (1)^7 * (1+4)^2 a positive number times a positive one, therefor positive
These numbers show the sign of the function on different intervals, for intervals of increase and decrease you must look at the derivative function.
f '(x) = x^6 * (x+4) * (9x+28)
An eighth-degree function with real zeros at x = -4, -28/9, 0
6x + 2 = 0
6x = -2
x = -2/6 = -1/3 = A
=======================================…
f(x) = x^7 * (x+4)^2
f '(x) = 7x^6*(x+4)^2 + x^7 * 2(x+4)*1
f '(x) = (x+4)*(2x^7 + 7x^6(x+4))
f '(x) = (x+4)*(9x^7 + 28x^6)
f '(x) = x^6 * (x+4) * (9x+28)
On [-15, 13]
f(x) = x^7 * (x+4)^2 equals zero at x = 0, -4
f(-5) = (-5)^7 * (-5+4)^2 a negative number times a positive one, therefor negative
f(-3) = (-3)^7 * (-3+4)^2 a negative number times a positive one, therefor negative
f(1) = (1)^7 * (1+4)^2 a positive number times a positive one, therefor positive
These numbers show the sign of the function on different intervals, for intervals of increase and decrease you must look at the derivative function.
f '(x) = x^6 * (x+4) * (9x+28)
An eighth-degree function with real zeros at x = -4, -28/9, 0
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1.f(x) = (3x+5)/(6x+2)
f(x) = [(3x + 5)*(6x - 2)]/[(6x + 2)*(6x - 2)]
f(x) = [9x^2 + 12x - 10]/[18x^2 - 2]
when denominator = 0 f(x) = infinity
18x^2 - 2 = 0
x^2 = 1/9 = + or - (1/3) = A
--------------------------------------…
f(x) = [(3x + 5)*(6x - 2)]/[(6x + 2)*(6x - 2)]
f(x) = [9x^2 + 12x - 10]/[18x^2 - 2]
when denominator = 0 f(x) = infinity
18x^2 - 2 = 0
x^2 = 1/9 = + or - (1/3) = A
--------------------------------------…
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i found out the answer, they told me to keep my dick to myself, so ill keep my cleverness too.