Which graph represents the polynomial function? f(x)=−x3+x2+9x−9

Mathematics

1 answer:

atroni [7]1 year ago

7 0

The curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)

<h3 /><h3>Graph of a polynomial</h3>

The graph of a polynomial function is a smooth continuous curve. The point where the curve intersects the x-axis is the zero of the polynomial.

A polynomial is also known to have a degree of 3 and above. Hence the given polynomial has a leading degree of 3 and expressed as:

f(x)=−x^3+x^2+9x−9

The graph of the function is as plotted below. From the function, you can see that the curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)

Learn more on polynomial graph here: brainly.com/question/10918240

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General Formulas and Concepts:

<u>Calculus</u>

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Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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Integration

Integrals
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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.$

Interval [0, π]

<u>Step 2: Find Arc Length</u>

[Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]: $\displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.$
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[Integral] Evaluate: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$