*Consider the function g(x)=x/x-7.
a)Summarize the increasing and decreasing intervals.
b)Compare the slopes of the tangents at the points where
i) x=7.5 and x=20
ii) x=6.5 and x= -20
SOMEONE DO THIS FOR ME PLEASE.....PLEASE DO THIS FOR ME PLEASE.....
Done for you 2 weeks ago
http://www.jiskha.com/display.cgi?id=1387130183
and even earlier
http://www.jiskha.com/display.cgi?id=1386792229
Steve found the derivative of the function for you, so for b) all you have to do is plug in the given values to get the slope of the tangents.
BTW, you said on Dec 16 that this had to be in the next morning. mmmmhhhh???
Yes Reiny i was post to hand this in in December but i was sick for lot of days so i couldn't. i have to hand this in tomorrow or my marks will go down. its already down. please help me. i tryed it but i couldn't do these two questions. please Reiny help me please. tell me the answers please, i have to get a good marks on this. please help.. please...
help i don't know how to do this. please help.
To summarize the increasing and decreasing intervals of the function g(x) = x/(x-7), we need to determine where the function is increasing or decreasing.
a) Increasing and Decreasing Intervals:
To find the intervals where the function is increasing or decreasing, we need to analyze the sign of the derivative of the function.
Step 1: Differentiate the function g(x) = x/(x-7) with respect to x:
To find the derivative, we can use the quotient rule:
g'(x) = [(x-7)(1) - x(1)] / (x-7)^2
= (x - 7 - x) / (x-7)^2
= -7 / (x-7)^2
Step 2: Determine where g'(x) is positive and negative:
To find the intervals where the function is increasing or decreasing, we need to consider the sign of g'(x).
For g'(x) = -7 / (x-7)^2, the sign of -7 does not change, so the sign of g'(x) will be determined by the sign of (x-7)^2.
(x-7)^2 is positive when x > 7 and negative when x < 7.
Thus, g'(x) = -7 / (x-7)^2 is negative when x > 7 and positive when x < 7.
Therefore, to summarize the increasing and decreasing intervals of g(x), we can say that the function is increasing for x < 7 and decreasing for x > 7.
b) Comparing the Slopes of Tangents:
To compare the slopes of the tangents at specific points, we need to find the first derivative and evaluate it at those points.
i) Tangents at x = 7.5 and x = 20:
For g(x) = x/(x-7), we have already found the first derivative, g'(x) = -7 / (x-7)^2.
To find the slope of the tangent at x = 7.5, we substitute x = 7.5 into g'(x):
g'(7.5) = -7 / (7.5 - 7)^2 = -7 / (0.5)^2 = -7 / 0.25 = -28
Similarly, to find the slope of the tangent at x = 20, we substitute x = 20 into g'(x):
g'(20) = -7 / (20 - 7)^2 = -7 / (13)^2 = -7 / 169
ii) Tangents at x = 6.5 and x = -20:
To find the slope of the tangent at x = 6.5, we substitute x = 6.5 into g'(x):
g'(6.5) = -7 / (6.5 - 7)^2 = -7 / (-0.5)^2 = -7 / 0.25 = -28
To find the slope of the tangent at x = -20, we substitute x = -20 into g'(x):
g'(-20) = -7 / (-20 - 7)^2 = -7 / (-27)^2 = -7 / 729
Therefore, we can compare the slopes of the tangents at the given points as follows:
i) At x = 7.5 and x = 20:
The slope of the tangent at x = 7.5 is -28, and the slope of the tangent at x = 20 is -7 / 169.
ii) At x = 6.5 and x = -20:
The slope of the tangent at x = 6.5 is -28, and the slope of the tangent at x = -20 is -7 / 729.