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3 years ago

15

Natalie is a softball coach. She has a pitching private lesson with Kasey. Kasey’s mom pays Natalie $11 per hour plus a $6 tip.

The correct equation was 11x + 6 = 39. So, how many hours was the lesson?

1 answer:

nevsk [136]3 years ago

6 0

Answer:

3

Step by Step:

Subtract the tip ($6) from the total ($39)

11x=33

Then divide 33 by 11, leaving you with the value of x.

x=3

The lesson was 3 hours long.

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Find the derivative of the function f(x) = (x3 - 2x + 1)(x – 3) using the product rule.

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Step-by-step explanation:

Hello, first, let's use the product rule.

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$f(x)=(x^3-2x+1)(x-3)=u(x) \cdot v(x)\\\\f'(x)=u'(x)v(x)+u(x)v'(x)\\\\ \text{ **** } u(x)=x^3-2x+1 \ \ \ so \ \ \ u'(x)=3x^2-2\\\\\text{ **** } v(x)=x-3 \ \ \ so \ \ \ v'(x)=1\\\\f'(x)=(3x^2-2)(x-3)+(x^3-2x+1)(1)\\\\f'(x)=3x^3-9x^2-2x+6 + x^3-2x+1\\\\\boxed{f'(x)=4x^3-9x^2-4x+7}$

Now, we distribute the expression of f(x) and find the derivative afterwards.

$f(x)=(x^3-2x+1)(x-3)\\\\=x^4-2x^2+x-3x^3+6x-4\\\\=x^4-3x^3-2x^2+7x-4 \ \ \ so\\ \\\boxed{f'(x)=4x^3-9x^2-4x+7}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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