Question

1. Solve for a and b given that:

2ab+10b^2=70

4ab^3 is as large (maximized) as possible

2. On what interval g(x) is concave up given that:

g(x) is a function and g"(x)= x^2+4x-4/(x^2+2x+4)^2

Answer #1

3) If A = 3
1 and B
= 1 7
0
-2
5 -1
Find
a) BA
b) determinant
B
c) Adjoint A
d)
A-1
4) Using matrix method solve the following simultaneous
equations
5x – 3y = 1
2x – 2y = -2
5) Given that f(x) = 6x - 5 g(x) = 3x +
4 and h(x) = 4x – 6
2
Find:-
i)...

solve the equations
a). 4x-(-3x-3) =2x +1-1/2x+1
b) 8x-x^2=2 solvee by completing square
c) x-2x^2=5 solve by quadraticformula

1. The critical point(s) of the function
2. The interval(s) of increasing and decreasing
3. The local extrema
4. The interval(s) of concave up and concave down
5. The inflection point(s).
f(x) = (x^2 − 2x + 2)e^x

Solve using Gaussian Elimination with back subsitution:
3x(1) - 2x(2) + x(3) =3
2x(1) + 4x(2) - 2x(3) = 2
4x(1) - 2x(2) - 3x(2) = -12

3. Given the function ?(?) = (x^3/3)-(3x^2/2)+2x:
a. Find all critical numbers.
b. Identify which, if any, critical numbers are local max or min
and explain your answer.
c. Find any inflection points and give the x value.
d. On the interval [0.6, 2.6] identify the absolute max and min,
if any. and justify your answer.
e. Give the interval where the curve is concave up and justify
your answer.

Let
h(x)=(x2+2x-3)(x2+4x+4)-1
Select one:
a. The function has a loc. max. at x=-3 and an inflection pt at
x=-1
b. The function has a horizontal asymptote y=1 and a vertical
asymptote x=-3.
c. The function has a horizontal asymptote y=1 and a vertical
asymptote x=-2.
d. The function has an abs. min. at x=-1 and is concave up on
(-∞, ∞).
e. The function has an abs. min. at x=-1 and is concave down on
(-∞, ∞)

Please solve all if possible
1. a) Find an equation of the tangent line to the graph of
y=x(x+1)^6 at the point where x=−2.
b) [2 points] State the coordinates of the x-intercept of the
line.
2. Find f(x) by solving the initial value
problem.
f′(x)=2−3x^ −2, f(3)=5.
3. Determine the intervals where the function f(x)=2x^2−1/4x^4
is increasing and decreasing, and also both coordinates of all
local extrema, if any. Label each extremum as a maximum or a
minimum.

1. solve the following (a) Solve −x 2 +2x = 1, by factorization.
(b) Solve 5x 2 −4x −2 = 0, by completing the square. (c) Solve 5x 2
+ x −1 = 0, by quadratic formula

1. The price of product A as a function of time is given by the
function f(t). Similarly, the function g(t) represents the price of
product B. We know that f is concave down and g is concave up.
Explain what the concavity represents in the terms of the evolution
of the price of A and B.
2. What is the maximum possible number of roots x4 + 4x + c = 0,
where c is a constant? Explaain.
3....

Given the following function: Y= (2x + 1)3 (x-1)
a) Determine where the function is increasing or decreasing. b)
Determine where the function is concave up or down

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