Math 121 Final ExamQuestions fully solved & verified for accuracy(A+graded)

Polynomials will be continuous at

all intervals(-infinity,+infinity)

Intervals on which the function is continuous for 8-9x-x^2

(-infinity,+infinity)

"Find its average rate of change over the interval

[−7, 1]" formula

f(x)-f(y)/y-x

f(x) = −x2 − 14x − 6

Find its average rate of change over the interval

[−7, 1]

ΔyΔx=-8

Marginal Cost =

dP/dX

Marginal Cost for P = −0.7x^3 + 30x^2 − 162.85x − 4000

−2.1x^2 + 60x − 162.85

Get the derivative using the chain rule

y = (8x^2 − 3)^3

"Show that the function is increasing and decreasing on the given open intervals"

Derivative, 0,0,-power,power

Find the first partial derivatives.

g(x, y) = ln(x^4 + y^4)

g(x)=

4x^3/x^4+y^4

"Consider the following.

f(x) = −4x2 + 32x"

Increasing and Decreasing will be

Increasing: (-infinity, CN)

Decreasing: (CN,infinity)

Consider the following.

f(x) = −4x2 + 32x

Increasing and Decreasing

Increasing: (-infinity,4)

Decreasing: (4,infinity)

y = −x3 + 9x2 − 3

Concave upward:

Concave downward:

(-infinity,3)

(3,infinity)

Relative max and min for sq rt # -x^2

Relative Max: 0,sq rt

Relative Min(Smaller Value):-sq rt, 0

Relative Min(Smaller Value):sq rt, 0

Relative Min and Max for sq rt 49 -x^2

Relative Max: 0, 7

Relative Min(Smaller Value):-7, 0

Relative Min(Smaller Value):7, 0

Sketch a graph of a function f having the given characteristics.

f(0) = f(2) = 0f '(x) < 0 if x < 1f '(1) = 0f '(x) > 0 if x > 1f ''(x) > 0

Positive U graph

"A campground owner plans to enclose a rectangular field adjacent to a river. The owner wants the field to contain 125,000 square meters. No fencing is required along the river. What dimensions will use the least amount of fencing"

x=

y=

y = sq rt (125,000 x 2)

x = sq rt (125,000 x 2)/2

To Find the number of units x that produces a maximum revenue R

Get derivative then solve for X

Find the number of units x that produces a maximum revenue R.

R = 102x^2 − 0.04x^3

x = 1700 Units

"Find the number of units x that produces the minimum average cost per unit C

in the given equation.

C = 0.001x3 + 6x + 250"

Find C bar, then C bar prime, then solve for X

Find the number of units x that produces the minimum average cost per unit C

in the given equation.

C = 0.001x^3 + 8x + 250

x = 50

Derivative of any f(x)=ln(#x)

1/x

Derivative of f(x)=ln(5x)

1/x

Derivative of f(x)=ln(7x)

1/x

Find the derivative of the function.

y = ln xx4

1-4ln(x)/x^5

When doing cubed root indefinite integrals will be

3/4 and 4/3

When finding the integral of e^# with nothing in front

All you do in add the fraction

Integral of e^5x-7

1/5e^5x-7+C

When using Log rule for integral when numerator is in the denominator answer will be

C+Ln(|numerator|)