First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have
Which means that the roots are
Next, we can expand the function definition:
In this form, it is much easier to compute the derivative:
If we evaluate the derivative in the points of interest, we have
This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation
is what we need. The three lines are:
This is the tangent at x = -2
This is the tangent at x = 0
This is the tangent at x = 1
Answer:
x=3
Step-by-step explanation:
0 = x -3
-x = -3
change the sign to positive so x= 3
Answer:
Company B pays more!
Step-by-step explanation:
All you have to do is...
25,000x10=250,000
+
1,600x10=16,000
= 266,000(company a)
28,500x10=285,000
+
700x10=7,000
= 292,000(company b)
1. Observe that the f(t) is change by 4 per time t => there's a acceleration of 4 => f''(t) = 4; Take the derivative of it we can get a velocity function. f'(t) = 4t + c. Since the velocity from 100 to 80 is -20 (average), this means at t = 0, f'(0) = -22 => f'(t) = 4t - 22; Take the derivative again to get the position function: f(t) = 2t^2 - 22t + d, here d = 100 should be trivial. So, the function that models the relationship is f(t) = 2t^2 - 22t + 100.
2. By the compound interest formula:
A = P (1 + r/n)^(nt) , since it's yearly, so n = 1;
results A(t) = 100 (1+0.12)^t.
3. The average rate of change is basically finding the slope, m = y1 - y2 / x1 - x2.
<span>Data
set X and data set Y both have the same interquartile range. If the
first quartile of data set X is less than the first quartile of data set
Y, then the third quartile of data set X is greater than the third
quartile of data set Y.
False</span>
