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son4ous [18]
3 years ago
8

HELP ME! THANK YOU! Explain your answer. I will mark brainlyest! Thanks!!!!

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
7 0

ANSWER:

C) (2, 5)

STEP BY STEP EXPLANATION:

You have to change it from point slope form to slope intercept form. then you have to substitute the ordered pairs for x & y & it'll show if it's a true statement or if it's a false statement.


y - 2 = 3(x - 1) --- POINT SLOPE FORM

y - 2 = 3x - 3

  + 2        + 2

y = 3x - 1 --- SLOPE INTERCEPT FORM


A: (-2, -2):

y = 3x - 1

-2 = 3(-2) - 1

-2 = -6 - 1

-2 = -7

NO


B: (-1, -2):

y = 3x - 1

-2 = 3(-1) - 1

-2 = -3 - 1

-2 = -4

NO


C: (2, 5):

y = 3x - 1

5 = 3(2) - 1

5 = 6 - 1

5 = 5

YES


Hope this helps you!!! :)

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Answer:

\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}

General Formulas and Concepts:

<u>Algebra I</u>

Terms/Coefficients

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<u>Calculus</u>

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  • Derivatives
  • Derivative Notation

Basic Power Rule:

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  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]:                                                                           \displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \frac{\sqrt{x}}{e^x}

<u>Step 2: Differentiate</u>

  1. Derivative Rule [Quotient Rule]:                                                                   \displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}
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  5. Rewrite:                                                                                                         \displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}
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Topic: AP Calculus AB/BC (Calculus I/I + II)

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