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A bird flies from a tree. At time t seconds, the bird’s height, y metres, above the horizontal ground is given by 𝑦 = 1/4𝑡^4 − 𝑡^2 + 5 , 0 ≤ 𝑡 ≤ 4

Find the rate of change of height of the bird in metres per second when 𝑡 = 1

ii) Determine, with a reason, whether the bird’s height above the horizontal ground is increasing or decreasing when 𝑡 = 1

 Dec 2, 2018

Best Answer 

 #1
avatar+4471 
+1

\(y = \dfrac 1 4 t^4 - t^2 + 5,~t\in [0,4]\)

 

\(\dfrac{dy}{dt} = t^3 -2t\\ \dfrac{dy}{dt}(1)= 1-2 = -1~m/s\)

 

\(\text{The fact that the sign of }\dfrac{dy}{dt} \text{ is negative shows that}\\ \text{the birds height is decreasing at }t=1\)

.
 Dec 2, 2018
 #1
avatar+4471 
+1
Best Answer

\(y = \dfrac 1 4 t^4 - t^2 + 5,~t\in [0,4]\)

 

\(\dfrac{dy}{dt} = t^3 -2t\\ \dfrac{dy}{dt}(1)= 1-2 = -1~m/s\)

 

\(\text{The fact that the sign of }\dfrac{dy}{dt} \text{ is negative shows that}\\ \text{the birds height is decreasing at }t=1\)

Rom Dec 2, 2018
 #2
avatar+792 
+1

thank you for the detailed explanation

YEEEEEET  Dec 2, 2018

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