(1 point) Consider the function e* f(x) = 54e Then f\'(a) The following question

Question

(1 point) Consider the function e* f(x) = 54e Then f'(a) The following questions ask for endpoints of intervals of increase or decrease for the function f(x) Write INF for 00, MINF for-00, and NONE if there are no intervals of that type The open interval of increase for f(x)is The open interval of decrease for f()is f(x) has a local minimum at f(r) has a local maximum at Then f"(x)- The following questions ask for endpoints of intervals of upward and downward concavity for the function f () Write INF for 00, MINF for-00, and write NONE if there are no intervals of that type The open interval of upward concavity for f(x) is The open interval of downward concavity for f(r)is f(x) has a point of inflection at

Explanation / Answer

A)

Use quotient rule to find derivative as

B)

Since (5 e^x)/(5 + e^x)^2 is always positive as e^x>0 for all x. hence increasing on

(-inf, inf)

C)

(5 e^x)/(5 + e^x)^2 is always postive, as e^x>0 for all x. hence decrease

NONE

d)

(5 e^x)/(5 + e^x)^2 will never be zero, as e^x>0 for all x. hence no critical point

NONE

e)

NONE

f) second derivative f"(x) is

g) concave up

-(e^x - 5) >0

e^x -5<0

e^x <5

x<ln(5)

hence

(-inf , ln(5))

f) Concave down

(ln(5), inf)

g)

(ln(5) , 1/2) or say x=ln(5)

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