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

2 Answers
Oct 22, 2017

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:)

Oct 22, 2017

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:)