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JulsSmile [24]
3 years ago
11

Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).

Mathematics
1 answer:
Soloha48 [4]3 years ago
5 0

Step 1: evaluate f(x+h) and f(x)

We have

f(x+h) = -(x+h)^2+6(x+h)-5 = -(x^2+2xh+h^2)+6x+6h-5

= -x^2-2xh-h^2+6x+6h-5

And, of course,

f(x)=-x^2+6x-5

Step 2: evaluate f(x+h)-f(x)

f(x+h)-f(x)=-x^2-2xh-h^2+6x+6h-5-(-x^2+6x-5)=-2xh-h^2+6h

Step 3: evaluate (f(x+h)-f(x))/h

\dfrac{f(x+h)-f(x)}{h}=-2x-h+6

Step 4: evaluate the limit of step 3 as h->0

f'(x) = \displaystyle \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}=-2x+6

So, we have

f'(1) = -2\cdot 1+6 = 4,\quad f'(2) = -2\cdot 2+6 = 2,\quad f'(3) = -2\cdot 3+6 = 0

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eimsori [14]
First we need to find k ( rate of growth)
The formula is
A=p e^kt
A future bacteria 4800
P current bacteria 4000
E constant
K rate of growth?
T time 5 hours
Plug in the formula
4800=4000 e^5k
Solve for k
4800/4000=e^5k
Take the log for both sides
Log (4800/4000)=5k×log (e)
5k=log (4800/4000)÷log (e)
K=(log(4,800÷4,000)÷log(e))÷5
k=0.03646

Now use the formula again to find how bacteria will be present after 15 Hours
A=p e^kt
A ?
P 4000
K 0.03646
E constant
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Plug in the formula
A=4,000×e^(0.03646×15)
A=6,911.55 round your answer to get 6912 bacteria will be present after 15 Hours

Hope it helps!
4 0
3 years ago
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Lucy was running a 10 mile race and the graph represents her running pace for the race. If the x-axis represents miles ran and t
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Have a great day!

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3 years ago
How do you solve 3 1/4- 1 7/8 step by step?
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Answer:

1 3/8.

Step-by-step explanation:

3 1/4 - 1 7/8

First convert to improper fractions:

3 1/4 = (3*4) + 1 / 4 =  13/4.

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The Lowest Common Multiple of 4 and 8 is 8 so we convert 13/4 to eighth's

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