Search & Filtering
Problem A.1
The graph below is made of three line segments:
-1 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
y
x
f(x)
g(x)
h(x)
The segments correspond to the following three functions:
f(x) = x − 2, g(x) = p
4 − (x − 6)2 + 2, h(x) = x − 6
Find the total length L of the graph between x = 2 and x = 10.
Problem A.2
Let f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative λ
(x) of the
following function with respect to x:
λ(x) = f(x) · g(x) + f(x) · h(x) − g(x) · h(x)
*Please give specific answers to both Problem A.1 & A.2
Problem A.1
The graph below is made of three line segments:
-1 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
y
x
f(x)
g(x)
h(x)
The segments correspond to the following three functions:
f(x) = x − 2, g(x) = p
4 − (x − 6)2 + 2, h(x) = x − 6
Find the total length L of the graph between x = 2 and x = 10.
Problem A.1
The graph below is made of three line segments:
-1 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
y
x
f(x)
g(x)
h(x)
The segments correspond to the following three functions:
f(x) = x − 2, g(x) = p
4 − (x − 6)2 + 2, h(x) = x − 6
Find the total length L of the graph between x = 2 and x = 10.
Problem A.1
The graph below is made of three line segments:
-1 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
y
x
f(x)
g(x)
h(x)
The segments correspond to the following three functions:
f(x) = x − 2, g(x) = p
4 − (x − 6)2 + 2, h(x) = x − 6
Find the total length L of the graph between x = 2 and x = 10.
Problem A.1
The graph below is made of three line segments:
-1 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
y
x
f(x)
g(x)
h(x)
The segments correspond to the following three functions:
f(x) = x − 2, g(x) = p
4 − (x − 6)2 + 2, h(x) = x − 6
Find the total length L of the graph between x = 2 and x = 10.
Find the smallest positive integer N that satisfies all of the following conditions:
• N is a square.
• N is a cube.
• N is an odd number.
• N is divisible by twelve prime numbers.
How many digits does this number N have?
Find the derivative of f(x)=(x4-3x2+7x).ex /ln(x2-3)
(1) Find and classify the extremes value of f(x) = 6x4 - 4x6 over the interval [ -2, 2].
(2) A retailer determines that the cost of ordering and storing units of a product can be modelled by C(x) = 3x + (2000/x), 0 ≤ x ≤ 200. Find the order size that will minimize ordering and storage cost.
The demand curve of a firm is p = 1200 - 21q and its total cost is C(q) =2q3-66q2+ 600q + 1000 where q is the output of the firm (in thousands).
(i) Derive an expression R (q ) , for the firm' s revenue function.
(ii) Derive an expression π(q) for the firm' s profit function.
(iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10,000 units?
(iv) Determine the level of output at which profit is maximized.
Determine the y-intercept, the zeros, the number of turning points, and the behavior of the graph and sketch the graph of the following polynomial functions.
1. P(x)=-2x³-22x²-60x
2. P(x)=6x³+5x²-2x-1
4. P(x)=x⁴+x³-10x²+8
#340153 on Dec 2023