Question

find maximum and minimum value of the function (a)y=25x^2+5-10x (b)y=9-(x-3)^2

Answer 1

Answer:

Explanation:

(a) Minimum value is 4.

(b) Maximum value is 9.

(a) y = 25x² + 5 - 10x

We differentiate the equation with respect to x.

To find critical point, we take  

50x - 10 = 0

x = 1/5

To find maxima or minima, we again differentiate w.r.t. x

which is positive for x = 1/5

This means y has minima at x = 1/5

To find minimum value we substitute x=1/5 in the given equation.

y = 1 + 5 - 2

y = 4 is the minimum value.

(b) y = 9-(x-3)²

y = 9 - [ x² - 6x + 9]

y = 6x - x²

Differentiating w.r.t. x,

To obtain critical point ,

6 - 2 x = 0

x = 3

To find whether maxima or minima we again differentiate w.r.t. x

= -2 which is negative for x=3

y has maximum value at x=3

Substituting x = 3 in given equation

y = 9 -(3-3)²

y = 9 is the maximum value