Read the following passage and answer the questions given below: elation between the height of the plant (y^ . in cm ) with respect to its exposure to is governed by the following equation y=4 x-1 2 x^2, where ' x ' is the number of days exposed to the sunlight, for x 3 (i) Find the rate of growth of the plant with respect to the number of days exposed to the sunlight. (ii) Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?

y=4 x-1 2 x^2 (i) The rate of growth of the plant with respect to the number of days exposed to sunlight is given by d y d x =4-x (ii) Let rate of growth be represented by the function g(x)=d y d x Now, g^ (x)=d d x (d y d x )=-1<0 g(x) decreases. So the rate of growth of the plant decreases for the first three days. Height of the plant after 2 days is y=4 2-1 2 (2)^2=6 ~cm.

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Read the following passage and answer the questions given below: elation between the height of the plant $\left(y^{\prime}\right.$ in cm $)$ with respect to its exposure to is governed by the following equation $y=4 x-\frac{1}{2} x^2$, where ' $x$ ' is the number of days exposed to the sunlight, for $x \leq 3$

(i) Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.

(ii) Does the rate of growth of the plant increase or decrease in the first three days?
What will be the height of the plant after 2 days?

✓

Answer

$y=4 x-\frac{1}{2} x^2$

(i) The rate of growth of the plant with respect to the number of days exposed to sunlight is given by $\frac{d y}{d x}=4-x$

(ii) Let rate of growth be represented by the function $g(x)=\frac{d y}{d x}$

Now, $g^{\prime}(x)=\frac{d}{d x}\left(\frac{d y}{d x}\right)=-1<0$

$\Rightarrow g(x)$ decreases.

So the rate of growth of the plant decreases for the first three days.

Height of the plant after 2 days is $y=4 \times 2-\frac{1}{2}(2)^2=6 \mathrm{~cm}$.

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Based on the above information, answer the following question.

Find the value of $\frac{\text{dP}}{\text{dt}}.$

$\frac{\text{Pr}}{1000}$
$\frac{\text{Pr}}{100}$
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$\log\Big(\frac{\text{P}}{\text{P}_0}\Big)=\frac{\text{rt}}{100}$
$\log\Big(\frac{\text{P}}{\text{P}_0}\Big)=\frac{\text{rt}}{10}$
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$12.728$ years
$14.789$ years
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$9.66\%$
$8.239\%$
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Order: The order of a differential equation is the order of the highest order derivative appearing in the differential equation.
Degree: The degree of differential equation is the power of the highest order derivative, when differential coefficients are made free from radicals and fractions. Also, differential equation must be a polynomial equation in derivatives for the degree to be defined.
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Order and degree of the differential equation $\text{y}\frac{\text{dy}}{\text{dx}}=\frac{\text{x}}{\frac{\text{dy}}{\text{dx}}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^3}$ are respectively.

$1, 1$
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Order $= 3,$ degree $=$ undefined.
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$3$
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