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sattari [20]
3 years ago
13

2x^2+3x-2, a=0 How do I find the derivative?

Mathematics
1 answer:
Ghella [55]3 years ago
5 0

You can use the definition:

\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h

Then if

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

we have

f(x+h) = 2(x+h)^2+3(x+h) - 2 = 2x^2 + 4xh+2h^2+3x+3h-2

Then the derivative is

\displaystyle f'(x) = \lim_{h\to0}\frac{(2x^2+4xh+2h^2+3x+3h-2)-(2x^2+3x-2)}h \\\\ f'(x) = \lim_{h\to0}\frac{4xh+2h^2+3h}h \\\\ f'(x) = \lim_{h\to0}(4x+2h+3) = \boxed{4x+3}

I'm guessing the second part of the question asks you to find the tangent line to <em>f(x)</em> at the point <em>a</em> = 0. The slope of the tangent line to this point is

f'(0) = 4(0) + 3 = 3

and when <em>a</em> = 0, we have <em>f(a)</em> = <em>f</em> (0) = -2, so the graph of <em>f(x)</em> passes through the point (0, -2).

Use the point-slope formula to get the equation of the tangent line:

<em>y</em> - (-2) = 3 (<em>x</em> - 0)

<em>y</em> + 2 = 3<em>x</em>

<em>y</em> = 3<em>x</em> - 2

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Answer:

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Step-by-step explanation:

Given as :

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Genevieve wants to verify that }(5x-20)-(4x-8) is equivalent to x. Which procedure can Genevieve follow to determine if
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They aren't equivalent

<h2>Explanation:</h2>

In order to determine whether the expression:

(5x-20)-(4x-8)

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x

Genevieve needs to follow these steps:

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5x-20-4x+8

Step 2. Combine like terms

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Step 3. Solve

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So:

x\neq x-12

Therefore, these two expressions aren't equivalent.

<h2>Learn more:</h2>

Writing expressions: brainly.com/question/13894833#

#LearnWithBrainly

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3 years ago
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Answer:

To drain the water tower it will take 36 hours.

Step-by-step explanation:

Given:

A 72,000 water tower is being drained, and in an hour 2000 gallons are drained.

Now, to calculate the hours it would take to drain total 72,000 gallons of water, we should divide the gallons of water drained in one hour by total gallons of water in the tower.

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Therefore, to drain the water tower it will take 36 hours.

6 0
3 years ago
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