Calculus Answers

Bongi supplies trays of fresh sandwiches to offices daily. Her daily fixed costs amount to R844

R844, while her variable cost is R27

R27 per tray. Bongi's total cost and marginal cost functions (in terms of the number of trays supplied, Q

Q) are given by

Bongi supplies trays of fresh sandwiches to offices daily. Her daily fixed costs amount to R844

R844, while her variable cost is R27

R27 per tray. Bongi's total cost and marginal cost functions (in terms of the number of trays supplied, Q

Q) are given by

Estimate the values of c that satisfy the conclusion of the Mean Value Theorem on the interval (0,8). Enter your answer as a comma-separated list. Round to one decimal.

Evaluate each of the following functions, find the indicated derivative

1. 𝑓(𝑥) = 𝑥^2 − 4𝑥 + 1; 𝑓′(2)

2. 𝑓(𝑥) = 𝑥^3 + 2; 𝑓′(−2)

3. 𝑓(𝑥) = 2𝑥^4 + 3𝑥^3 − 2𝑥 + 7; 𝑓′(0)

4. f(x) = √2x + 7; f'(1)

5. f(x) = 1 + √x^2 + 3x +6; f'(2)

6. f(x) = x/x+4 ; f'(-3)

7. f(x) = x^2 +3/4 - x^2 ; f'(-1)

8. f(x) = √x + 3/x - 4 ;f'(1)

9. f(x) = 3- √ 5x - 9/2x - 1 f'(2)

10. f(x) = 2x^2 + 3 - 1; f'(-1)

A. Identify if the equation f(x)=x⁵-2x⁴+x³-3x²-x+5 has a solution on each given closed interval. Show your proof using the intermediate value theorem.

1.[-2,1]

2.[-1,0]

3.[0,1]

4.[1,2]

5.[2,4]

B. Sketch the graph of f(x)=4-x² and then find the absolute extreme values of the interval [-3,1]

Show the graph and determine if the given function is continuous on each of the given intervals.

1. f(x)=4x²-x+6; (-infinite, 0)

2.f(x)=4/x-5;(-5,5)

3.f(x)=√x-1;(1,+infinite)

4.f(x)=-|-5x|;(-1,+infinite)

What is the axis of symmetry for the graph of y=2x2-4x+2

Trace the following curves (x^2+y^2)x=2x^2+y^2

If ln=int_zero to infinity e^-x sin^n (x)dx,prove that (1+n^2)ln=n(n-1)ln-2 for n≥2.

Calculate the volume of the solid formed by revolving about the line y=1 the region bounded by the parabola

𝑥

2 = 4𝑦 and that line. Take the rectangular elements of area parallel to the axis of revolution.