Question

Local extreme Value for each of the Following A) F(x)=x^² - 4x² +5​

Answer 1

max{x²-4x²+5} = 5 at x = 0

Explanation:

1. Find the critical numbers by finding the first derivative of f(x), set it to 0 and solve for x.

`f'(x)=0`

We get:

`f(x) = -3x^2+5\\f'(x) = -6x\\-6x = 0\\x = 0`

So the critical number is x = 0.

2. Evaluate the first derivative by plugging in the critical number and see if the derivative is positive or negative on both sides:

`f'(x)` is positive when the x < 0 (for example: -6*(-1)=+)

`f'(x)` is negative when the x > 0 (for example: -6*(1)=-)

Therefore, you have a local maximum.

Now just get the Y value by plugging in the critical number in the original function.
`f(0)=5`

local maximum is (0,5)