Question

Let f ( x ) = − 4 x 2 + 280 x − 1500. Determine the critical numbers.

Answer #1

The answer sheet has two pages.it is the first pagesecond/last page

Let f(x)=x^4(x−5)^8 / (x^2+5)^4
Use logarithmic differentiation to determine the
derivative.
f '(x) =

Let f(x) = 4/x and g(x) = x + 4. Determine (f 0 g)(x) and its
domain.

Let f(x)= x^7(x−6)^8 / (x^2+4)^6
Use logarithmic differentiation to determine the
derivative.

Determine the critical numbers?
f(x) = x^3 + 5/2x^2 - 28x

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

f(x)= -4x/ x^2+4
i think i found the first dervivative: f'(x)=
(4x^2-16)/(x^2+4)^2
but im not sure if thats right and then i get confused after
that on how i find the critical numbers: x=____
i think i got x=2 for the critical number
then i am supposed to find where it is increasjng and
decreasing and i dont understand the steps on how to find that out-
i understand the number line but how do you plug in the
numbers...

Analyze and sketch the graph of the function f(x) = (x −
4)2/3
(a) Determine the intervals on which f(x) is increasing /
decreasing
(b) Determine if any critical values correspond to a relative
maxima / minima
(c) Find possible inflection points
(d) Determine intervals where f(x) is concave up / down

Let f(x) be a function that is continuous for all real numbers
and assume all the intercepts of f, f' , and f” are given below.
Use the information to a) summarize any and all asymptotes,
critical numbers, local mins/maxs, PIPs, and inflection points, b)
then graph y = f(x) labeling all the pertinent features from part
a. f(0) = 1, f(2) = 0, f(4) = 1 f ' (2) = 0, f' (x) < 0 on (−∞,
2), and...

Let
f(x)=ln[x^3(x+5)^5(x^2+4)^6]
f '(x)=

Let f(x)= (x-2)/(x^2-9)
A. find the x and y-intercepts
B. find the vertical and horizontal asymptote if any
C. find f'(x) and f''(x)
D. find the critical values
E. determine the interval of increasing, decreasing, and find
any relative extreme
F. determine the interval which f(x) is concave up, concave
down, and any points of inflection

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