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Pepsi [2]
3 years ago
11

Which is the rate of change for the interval between –6 and –3 on the x-axis?

Mathematics
2 answers:
Naya [18.7K]3 years ago
8 0
A. -2 is the correct answer for the rate of change
aalyn [17]3 years ago
7 0

Answer:

A is the answer to this question. Hope this helps!

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How to differentiate ?
Bas_tet [7]

Use the power, product, and chain rules:

y = x^2 (3x-1)^3

• product rule

\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}

• power rule for the first term, and power/chain rules for the second term:

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}

• power rule

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3

Now simplify.

\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) =  \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)

Differentiate both sides and you end up with the same derivative:

\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2

7 0
3 years ago
Decrease £19064.67 by 19.5%
8_murik_8 [283]
Answer = £15347.06

100 - 19.5 = 80.5

80.5 / 100 = 0.805

19064.67 x 0.805 = £15347.06
8 0
3 years ago
Read 2 more answers
How do u find slope on the graph
Shkiper50 [21]

Answer:

you get 2 coordinates x one, y one, x two, and y two and then do rise over run which is y two - y one over x two - x one say x one is 4 and y one is 7 and x two is 8 and y two is 13 you say 13-7=6 and 8-4=4 so it is 6/4 hope that makes sense

7 0
3 years ago
How many grams must be adde to 970g to make 1 and a half kg
madam [21]

Answer:

530 grams

Step-by-step explanation:

970 grams = 0.970 kg

1 kg = 1000 grams

Thus: 500+30 = 530 grams

3 0
3 years ago
Pay the bill using the fewest possible bills/coins
marysya [2.9K]

Answers:

Open the pdf below and youll find what you need. also do the largest bills you can.

Download pdf
4 0
3 years ago
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