Answer:
max{x²-4x²+5} = 5 at x = 0
Step-by-step explanation:
1. Find the critical numbers by finding the first derivative of f(x), set it to 0 and solve for x.
[tex]f'(x)=0[/tex]
We get:
[tex]f(x) = -3x^2+5\\f'(x) = -6x\\-6x = 0\\x = 0[/tex]
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:
[tex]f'(x)[/tex] is positive when the x < 0 (for example: -6*(-1)=+)
[tex]f'(x)[/tex] 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. [tex]f(0)=5[/tex]
local maximum is (0,5)
