Question

a.) Find the following limit. lim x→−∞ x^3 - sqrt(4x^6-3x)/7x^3+x b.) Sketch the graph of a...

a.) Find the following limit.

lim x→−∞ x^3 - sqrt(4x^6-3x)/7x^3+x

b.) Sketch the graph of a function f(x) that has all of the following features:

f ' (x) > 0 on the intervals (−∞, −4) ∪ (3,∞).

f ' (x) < 0 on the intervals (−4, −1) ∪ (−1, 3).

f '' (x) > 0 on the intervals (−∞, −4) ∪ (−4, −2) ∪ (−1, 4).

f '' (x) < 0 on the intervals (−2, −1) ∪ (4,∞).

x-intercepts when x = −5, −2, and 0

A local minimum at (3, −3).

Inflection points at (−2, 0) and (4, −2.5).

lim x→−4 f(x) = ∞.

lim x→−1− f(x) = −∞, lim x→−1+ f(x) = ∞.

lim x→±∞ f(x) = −2.

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