Question
State the method of obtaining maximum or minimum value of a function.
✓
Answer
Suppose, $y = f(x).$
- Find $\frac{d y}{d x} = f’ (x)$ for the given function.
- Solve the equation $\frac{d y}{d x} = 0$ and obtain the values of $x.$ These values are the stationary points of function.
- Obtain second order derivative $\frac{d^{2} y}{d x^{2}} = f”(x).$
- At the stationary value of $x$ if $\frac{d^{2} y}{d x^{2}} > 0 ($Positive$),$ then that value of $x$ gives the minimum value of the function. Putting this value of $x$ In the function, the minimum value of the function is obtained.
- At the stationary value of $x$ if $\frac{d^{2} y}{d x^{2}} < 0 ($Negative$),$ then that value of $x$ gives the maximum value of the function. Putting this value of $x$ in the function, the maximum value of the function is obtained.
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Similar questions
Answer the following questions from the given data.
$(i)$ If $b_{y x}=0.8, u=x-10, v=y+15$ then find the value of $b_{v i r}$.
$(ii)$ If $u=\frac{x-5}{3}, v=\frac{y-8}{5}$ and $b_{v u}=0.54$ then find the value of $b_{y x}$.
$(iii)$ If $u=5(x-40), v=\frac{y-50}{10}$ and $b_{y x}=0.25$ then find the value of $b_{ v }$.
→$(i)$ If $b_{y x}=0.8, u=x-10, v=y+15$ then find the value of $b_{v i r}$.
$(ii)$ If $u=\frac{x-5}{3}, v=\frac{y-8}{5}$ and $b_{v u}=0.54$ then find the value of $b_{y x}$.
$(iii)$ If $u=5(x-40), v=\frac{y-50}{10}$ and $b_{y x}=0.25$ then find the value of $b_{ v }$.
The following results are obtained for a bivariate data.
Obtain the regression line of $Y$ on $X.$
→Obtain the regression line of $Y$ on $X.$
$\lim _{x \rightarrow-1} \frac{x^3+1}{x+1}$
→For two related variables $X$ and $Y, \sum (x – x̄)^2 = 80, \sum (x – \bar X ) (y – ȳ) = 60, x̄ = 8, ȳ = 10.$ Obtain the regression line of $Y$ on $X.$
→If by $y_x=0.8$, then find the value of $b_{v u}$ for the following $u$ and $v$.
$(i)\ u=x-105$ and $v=y-90$.
$(ii)\ u=\frac{ x -1400}{100}$ and $v=\frac{ y -750}{50}$
$(iii)\ u=10(x-4.6)$ and $v=y-75$ OR
The following information is obtained to study the relationship between average rainfall $($in $cm.)$ and the yield of Maize $($in quintal per hectare$)$ in different taluka of Gujarat.
Correlation coefficient $= 0.82$ Obtain the regression lire of $Y$ on $X.$ Estimate the yield of maize when the rainfall is $60 \ cm.$
→$(i)\ u=x-105$ and $v=y-90$.
$(ii)\ u=\frac{ x -1400}{100}$ and $v=\frac{ y -750}{50}$
$(iii)\ u=10(x-4.6)$ and $v=y-75$ OR
The following information is obtained to study the relationship between average rainfall $($in $cm.)$ and the yield of Maize $($in quintal per hectare$)$ in different taluka of Gujarat.
| Particulars | Rainfall $(cm.)$ $(X)$ |
Yield Of size $(Y)$ $($Quintal per hectare$)$ |
| Mean | $82$ | $180$ |
| Variance | $64$ | $225$ |
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