Question

# question #1: Consider the following function. f(x) = 16 − x2,     x ≤ 0 −7x,     x...

question #1: Consider the following function.

f(x) =

 16 − x2, x ≤ 0 −7x, x > 0

(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)
x =

(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

 increasing decreasing

question#2:

Consider the following function.

f(x) =

 2x + 1, x ≤ −1 x2 − 2, x > −1

(a)

Find the critical numbers of f. (Enter your answers as a comma-separated list.)

x =

(b)

Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

increasing

decreasing

(c)

Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)

relative maximum

(x, y)

=

relative minimum

(x, y)

question#3:Consider the function on the interval (0, 2π).

f(x) = sin(x) cos(x) + 6

(a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.)

 increasing decreasing

(b) Apply the First Derivative Test to identify all relative extrema.

relative maxima     (x, y) = (smaller x-value)
(x, y) = (larger x-value)
relative minima (x, y) = (smaller x-value)
(x, y) = (larger x-value)

question number 4:

Consider the function on the interval (0, 2π).

f(x) = 5 sin2(x) + 5 sin(x)

(a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.)

 increasing decreasing

(b) Apply the First Derivative Test to identify all relative extrema.

relative maxima     (x, y) =

π2​,10

(smaller x-value)
(x, y) =

3π2​,0

(larger x-value)
relative minima (x, y) =    (smaller x-value)
(x, y) =    (larger x-value)

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