Question

the function y is given by 20x-2x^2 then find minimum value of function​

Answer 1

Answer:

the maximum value is 7 at x = 2. Now let us check this in the graph. Checking : y = 4x - x2 + 3.

Answer 2

Answer:

The minimum value of function is exists at x = 5 and the value = 50

Explanation:

At Maximum and Minimum points the derivative of a function is zero

Note:

• if the value of second order differential equation is less than zero the function has a maximum value
• if the value of second order differential equation is greater than zero the function has a minimum value

Given function f(x) = y

y = 20*x - 2*x²

differentiating with x on both sides

dy/dx = d/dx ( 20*x - 2*x² )

dy/dx = d/dx (20*x) - d/dx (2*x²)

dy/dx = 20 - 2*(2x)

dy/dx = 20 - 4x    (first order differentiation)

20 - 4x = 0  (derivative at maximum or minimum points is zero (dy/dx = 0))

4x = 20

x = 20 / 4

x = 5

substituting value of x in function we get the minimum value

f(x) = 20*x - 2*x²

f(5) = 20*5 - 2*(5)²

     = 100 - 2*25

     = 100 - 50

     = 50

Hence, minimum value of function = 50

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