Help me with calc!

lovemath.docx

1. on [-5, 3]

a) Determine the critical points of f(x).

b) Determine where the function f(x) is increasing and / or decreasing.

c) Determine all relative (local) minimums and / or maximums points of f(x).

d) Determine where the function f (x) is concave up / concave down.

e) Determine all inflection points of f(x).

f) Determine the absolute (global) minimum and maximum points of f(x).

g) Sketch the general shape of the graph for f.

2. A campground owner has 1400 m of fencing. He wants to enclose a rectangular field bordering a river, with

no fencing needed along the river. Determine the dimensions that would enclose the maximum area.

3. Sketch a graph of g(x) with the following characteristics:

Continuous for all real numbers

for and (1, 3)

for (-6, 1) and

for (-6, 3)

for and

f(0) = 2

4. Determine the linear approximation to f (x) = 4x3 -2x + 1 at x = 4 and use it to approximate f(4.3).

Compare this to the actual f(4.3)

5. Use a linear approximation to estimate . Compare to the exact answer.

6. Solve the initial value problem. (1, 7)

7. Determine y if y’(2) = 6, and y(3) = -4.

(,6)

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