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# A bird flies from a tree. At time t seconds

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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

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

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

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

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Dec 2, 2018

#1
+1

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

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

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

Rom Dec 2, 2018
#2
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thank you for the detailed explanation

YEEEEEET  Dec 2, 2018