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

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

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Answer 1 · 2017-10-22T08:57:39

Let's see.

Explanation:

Let the function given be $y$ $y$ such that $\to$ $rarr$

$y = f (x) = - x^{2} + 2 x + 3$ $y=f(x)=-x^2+2x+3$

Now differentiating w.r.t $x$ $x$ :

$\frac{d y}{d x} = - 2 x + 2$ $dy/dx=-2x+2$

Now the second order derivative is :

$\frac{d^{2} y}{{d x}^{2}} = - 2$ $(d^2y)/dx^2=-2$

Now, the second order derivative is negative.

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

Therefore the point of maxima is $- 2$ $-2$ .

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

Hope it Helps:)

Answer 2 · 2017-10-22T08:57:39

Let's see.

Explanation:

Let the function given be $y$ $y$ such that $\to$ $rarr$

$y = f (x) = - x^{2} + 2 x + 3$ $y=f(x)=-x^2+2x+3$

Now differentiating w.r.t $x$ $x$ :

$\frac{d y}{d x} = - 2 x + 2$ $dy/dx=-2x+2$

Now the second order derivative is :

$\frac{d^{2} y}{{d x}^{2}} = - 2$ $(d^2y)/dx^2=-2$

Now, the second order derivative is negative.

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

Therefore the point of maxima is $- 2$ $-2$ .

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

Hope it Helps:)

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

2 Answers

Explanation:

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