question #1: Consider the following function.
f(x) =
16 − x^{2},  x ≤ 0 
−7x,  x > 0 
(a) Find the critical numbers of f. (Enter your answers
as a commaseparated 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 
x^{2} − 2,  x > −1 
(a)
Find the critical numbers of f. (Enter your answers as a commaseparated 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) =



(x, y) =



relative minima  (x, y) =



(x, y) =


question number 4:
Consider the function on the interval (0, 2π).
f(x) = 5 sin^{2}(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 


(x, y) =

3π2,0 


relative minima  (x, y) =



(x, y) =


Get Answers For Free
Most questions answered within 1 hours.