3 years ago

Witch of the following is a true statement about a circle inscribed in a regular polygon

Mathematics

1 answer:

ss7ja [257]3 years ago

4 0

The area of the circle is equal to the area of the polygon

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3 years ago

Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).

Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>

The critical points of a function are the values of x for which:

$f^{\prime}(x) = 0$

In this problem, the function is:

$f(x) = x^3 + ax^2 + b$

Hence, the derivative is:

$f^{\prime}(x) = 3x^2 + 2ax$

Then:

$f^{\prime}(x) = 0$

$3x^2 + 2ax = 0$

$x(3x + 2a) = 0$

$x = 0$

$3x + 2a = 0$

$3x = -2a$

$x = -\frac{2a}{3}$

Since the critical point is at x = 2, we have that:

$-\frac{2a}{3} = 2$

$-2a = 6$

$2a = -6$

$a = -3$

Then:

$f(x) = x^3 - 3x^2 + b$

Critical point at (2,3) means that when $x = 2, y = 3$ , then:

$3 = 2^3 - 3(2)^2 + b$

$8 - 12 + b = 3$

$b = 7$

You can learn more about the critical point concept at brainly.com/question/2256078

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2 years ago