Consider the function and its derivatives: f(x) = ex x² Curve Sketching 3 Check f'(x) = (x - 2). ex x3 f" (x) = (x² - 4x+6) · ex X4 a) What is the domain of f in interval notation? oo(-inf, inf) (-?, ?) b) Find the set of all critical points of f. {0} {0} c) Find the intervals of increase and decrease for f. f is increasing on: f is decreasing on: d) Find the intervals of concavity for f. f is concave up on: f is concave down on: e) Find the set of all x-values of the inflection points of f.

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Consider the function and its derivatives:

f (x) = \frac{e ^{x}}{x ^{2}}, f^{?} (x) = \frac{( x ? 2 ) ? e ^{x}}{x ^{3}} f^{??} (x) = \frac{( x ^{2} ? 4 ? x + 6 ) ? e ^{x}}{x ^{4}}

a) What is the domain of

f

in interval notation? b) Find the set of all critical points of

f

.

{0}

c) Find the intervals of increase and decrease for

f

.

f

is increasing on:

f

is decreasing on: d) Find the intervals of concavity for

f

.

f

is concave up on:

f

is concave down on: e) Find the set of all

x

-values of the inflection points of

f

.

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