To find f'(3) (f prime of 3), you must find f' first. f' is the derivative of the function f(x).
Finding the derivative of f(x) = 2x⁴ requires the use of the power rule.
The power rule for derivatives is ![\frac{d}{dx} [x^{n} ] =nx^{n-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bx%5E%7Bn%7D%20%5D%20%3Dnx%5E%7Bn-1%7D)
. In other words, you bring the exponent forward and multiply it by the coefficient of the term, and then you subtract 1 from the original exponent.
f'(x) = 
(2x⁴)
f'(x) = 2(4)x³
f'(x) = 8x³
Now, to find f'(3), plug 3 into your derivative.
f'(3) = 8(3)³
f'(3) = 216
<h3>Answer:</h3>
f'(3) = 216
Answer:
$178.3
Step-by-step explanation:
The value of a car is $20,000
The car loses 10.7% of its value yearly
Since there are 12 months in a year then 10.7% can be represented as
10.7%/12
= 0.8916%
Therefore the approximate monthly decrease in value can be calculated as follows
= $20,000×0.8916/100
= $20,000×0.008916
= $178.3
Hence the approximate monthly decrease in value is $178.3
The general form for a line through two points (a,b) and (c,d) is
(c-a)(y-b)=(d-b)(x-a)
This is better than the slope forms because it works in the no slope case, as does the standard form.
If you haven't seen it before, it works because when (x,y)=(a,b) we get (c-a)(b-b)=(d-b)(a-a), both sides zero, and when (x,y)=(c,d) we get (c-a)(d-b)=(d-b)(c-a), clearly equal sides.
Here we have
(0 - -5)(y - 0) = (-9 - 0)(x - - 5)
5y = -9(x+5)
5y = -9x - 45
9x + 5y = -45
Ironically there are two standards for standard form; one with the constant alone on the right and one with the whole thing equal to zero. I like the constant alone.
Answer: 9x + 5y = -45
Check:
We check each point is on the line
(-5,0)
9(-5) + 5(0) = -45, good
(0, -9)
9(0) + 5(-9) = -45, good again
Answer:
<h2>d = 8</h2><h2>g = 2</h2>
Step-by-step explanation:
8d + 4 = 5d + 28
Group like terms
That's
8d - 5d = 28 - 4
3d = 24
Divide both sides by 3
d = 8
Cross multiply
we have
7(7g + 8) = 38.5(4)
49g + 56 = 154
49g = 154 - 56
49g = 98
Divide both sides by 49
g = 2
Hope this helps you
This is just like the other problem. The coefficient infront of the b which is "2" is your constant of proportionality. It makes the relationship between the number of bulbs and flowers signaling that for every flower there has to be 2 bulbs.
