Question

2
7 4
1
English
Review Later
Calculate maximum or minimum value of the
function y = 25x2 + 5 - 10x
1
Ymin = 4
2
ymax = 8
3
Ymin = 8
Ymax = 4​

Answer 1

Answer:

sorry I don't know this answer. plz you will try for next.

Answer 2

Given :

Function

$y = 2 5{x}^{2} + 5 - 10x$

To find :

Extreme (minimum or maximum) value of function.

Solution :

Given function is :

$y = 2 5{x}^{2} + 5 - 10x$

To get the extreme value of function.

To get the extreme value of function.We have to first differentiate y with respect to x to get the value of x at which y will get extreme value.

So,

$\frac{dy}{dx} = 50x - 10$

Putting the differentiation value is equal to 0 to get the extreme point :

50x - 10 = 0

50x = 10

So

$x = \frac{10}{50} = \frac{1}{5} = 0.2$

To know that the extreme point is maxima of minima,

we have to differentiate the function twice.

If putting the value of extreme point (got after differentiating once) inthe function got after double differentiation is :

positive then it is minima .

negative then it is maxima.

So

$\frac{ {d}^{2}y }{d {x}^{2} } = 50$

as it is a positive value.

It means It has a minimum value for x = 0.2

So, minimum value of function y :

$y = f(0.2) = 25( {0.2}^{2} ) + 5 - 10(0.2) \\ = 1 + 5 - 2 = 4$

Minimum value of function y = 4

So correct option is (1)