Question

What are the extrema of `f(x)=3+ 2x -x^2`?

Answer 1

Let's see.

Explanation:

Let the function given be `y` such that `rarr`

`y=f(x)=-x^2+2x+3`

Now differentiating w.r.t `x`:

`dy/dx=-2x+2`

Now the second order derivative is :

`(d^2y)/dx^2=-2`

Now, the second order derivative is negative.

Hence, the function only has an extrema & no minima.

Therefore the point of maxima is `-2`.

The maximum value of the function is `f(-2)`.

Hope it Helps:)

Answer 2

Let's see.

Explanation:

Let the function given be `y` such that `rarr`

`y=f(x)=-x^2+2x+3`

Now differentiating w.r.t `x`:

`dy/dx=-2x+2`

Now the second order derivative is :

`(d^2y)/dx^2=-2`

Now, the second order derivative is negative.

Hence, the function only has an extrema & no minima.

Therefore the point of maxima is `-2`.

The maximum value of the function is `f(-2)`.

Hope it Helps:)