Question 5(3 points)

Lety=f(t),t

{"version":"1.1","math":"$\ge$"}0, be the solution to initial value problemy'=y²

{"version":"1.1","math":"$-$"}a²,

{"version":"1.1","math":"$-$"}ay(0) =y₀a> 0 is a constant.Which one of the following statements is true?

Question 5 options:

a)

y(t) is decreasing and its graph is concave up for allt

{"version":"1.1","math":"$\ge$"}0

b)

y(t) is increasing for allt

{"version":"1.1","math":"$\ge$"}0.There existst₁> 0 such that the graph ofy(t) is concave up when 0 tt₁, and it is concave down whent>t₁.

c)

y(t) is decreasing for allt

{"version":"1.1","math":"$\ge$"}0.There existst₁> 0 such that the graph ofy(t) is concave down when 0 tt₁, and it is concave up whent>t₁.

d)

y(t) is increasing and its graph is concave up for allt

{"version":"1.1","math":"$\ge$"}0

e)

y(t) is decreasing and its graph is concave down for allt

{"version":"1.1","math":"$\ge$"}0

f)

y(t) is increasing and its graph is concave down for allt

{"version":"1.1","math":"$\ge$"}0

Question 5 (3 points) J Saved Lety :f(t), t Z 0, be the solution to initial value problem y' :y2 a2, a 0 is a constant. Which one of the following statements is true? 6) a) ylt) is decreasing and its graph is concave up for all t Z 0 O b) y(t) is increasing for all t Z 0. There exists t1 > 0 such that the graph of y(t) is concave up when 0 t1. 0 C) y(t) is decreasing for all I 2 0. There exists II > 0 such that the graph of y(t) is concave down when 0 t1. Q d) y(t) is increasing and its graph is concave up for all t Z 0 O e) y(t) is decreasing and its graph is concave down for all t Z 0 O f) ylt) is increasing and its graph is concave down for all t Z O