Question

Let the function f be defined as f(x) = x 2 − x + 30, where x is the number of widgets (in thousands) produced and f(x) is the amount (in dollars) of revenue for your company.

(a) Find the average rate of change of f between x = 3 and x = 4. Give units for your answer.

(b) Graph the function, the points, and the secant line between them.

(c) Explain in your own words what the meaning of the average rate of change is for this scenario. Be specific for full credit.

Answer #1

1. Let f be the function defined by f(x) = x
2 on the positive real numbers. Find the
equation of the line tangent to the graph of f at the point (3,
9).
2. Graph the reflection of the graph of f and the line tangent to
the graph of f at the point
(3, 9) about the line y = x.
I really need help on number 2!!!! It's urgent!

Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where
a, b, and c are constants. The graph of f has a vertical asymptote
at x=1, and f has a removable discontinuity at x=−2.
(a) Show that a=2 and b=−4.
(b) Find the value of c. Justify your answer.
(c) To make f continuous at x=−2, f(−2) should be defined as
what value? Justify your answer.
(d) Write an equation for the horizontal asymptote to the graph
of f. Show the...

Consider the function f(x) = √x and
the point P(4,2) on the graph f.
a)Graph f and the secant lines passing through the
point P(4, 2) and Q(x,
f(x)) for x-values of 3, 5, and 8.
b) Find the slope of each secant line. (Round your answers to
three decimal places.)
(line passing through Q(3, f(x)))
(line passing through Q(5, f(x)))
(line passing through Q(8, f(x)))
c)Use the results of part (b) to estimate the slope of the
tangent line...

Let F be the defined by the function F(x, y) = 3 + xy - x - 2y,
with (x, y) in the segment L of vertices A (5,0) and B (1,4). Find
the absolute maximums and minimums.

Let the function f and g be defined as f(x) = x/ x − 1 and g(x)
= 2 /x +1 . Compute the sum (f + g)(x) and the quotient (f/g)(x) in
simplest form and describe their domains.
(f + g )(x) =
Domain of (f+g)(x):
(f/g)(x) =
Domain of (f/g)(x):

Q6/
Let X be a discrete random variable defined by the
following probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Give P(4≤ X < 8)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q7/
Let X be a discrete random variable defined by the following
probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Let F(x) be the CDF of X. Give F(7.5)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q8/
Let X be a discrete random variable defined by the following
probability function :
x
2
6...

Consider the function f(x)=5x−4 and find the following:
a.) The average rate of change between the points (−1,f(−1)) and
(2,f(2)).
b.) The average rate of change between the points (a,f(a)) and
(b,f(b)).
c.) The average rate of change between the points (x,f(x)) and
(x+h,f(x+h)).

Suppose f(x) = (2/x) + 5 .
a. *Graph this function.
b. *Find the equation of the secant line to f(x) on the interval
[1, 3]. Call this line g(x). Add g(x) to your graph
c. Find the equation of the tangent line to f(x) at the point
(2,6). Call this line h(x). Add h(x) to your graph.
Please neatly show your work.

Let f : [0,∞) → [0,∞) be defined by, f(x) := √ x for all x ∈
[0,∞), g : [0,∞) → R be defined by, g(x) := √ x for all x ∈ [0,∞)
and h : [0,∞) → [0,∞) be defined by h(x) := x 2 for each x ∈ [0,∞).
For each of the following (i) state whether the function is defined
- if it is then; (ii) state its domain; (iii) state its codomain;
(iv) state...

1 (a) Let f(x) be the probability density function of a
continuous random variable X defined by
f(x) = b(1 - x2), -1 < x < 1,
for some constant b. Determine the value of b.
1 (b) Find the distribution function F(x) of X . Enter the value
of F(0.5) as the answer to this question.

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