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SVEN [57.7K]
3 years ago
15

What is the rate of change between the interval of x = 3 pi over 2 and x = 2π?

Mathematics
2 answers:
galina1969 [7]3 years ago
5 0
Check the picture below.

\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
x_1=\frac{3\pi }{2}\\
x_2=2\pi 
\end{cases}\implies \cfrac{f(2\pi )-f\left( \frac{3\pi }{2} \right)}{2\pi -\frac{3\pi }{2} }\implies \cfrac{3-1}{\frac{4\pi -3\pi }{2}}\implies \cfrac{2}{\quad \frac{\pi}{2}\quad }\implies \cfrac{4}{\pi }

Sati [7]3 years ago
3 0

Answer:

The answer is 4/pi

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First find f′ and then find f. f′′(x)=3x^3+6x^2−x+2, f′(1)=9, f(1)=−7. <br> f′(x)= <br> f(x)=
Vadim26 [7]
I haven't learned antiderivitives yet but I can try to logic it

<span>First find f′ and then find f. f′′(x)=3x^3+6x^2−x+2, f′(1)=9, f(1)=−7.

we reverse chain rule

3x^3, we know that it was a 4th degree thing, and the coefient is 3, so
4*what=3?, answer is 3/4
3/4x^4

6x^2
we know it was x^3, and the coefient is now 6 so
3*what=6? what=2
2x^3

-1x, the power was 2 and coefient is now -1, so
2 times what=-1?, -1/2
-1/2x^2

2, that is from 2x

so
</span>
<span>3/4x^4+2x^3-1/2x^2+2x=f'(x)
test x=1
(3/4)(1)+2(1)-(1/2)(1)+2(1)=
3/4+2-2/4+2=
4 and 1/4 we need to get it to 9
4 and 1/4 +what=9
answer is 4 and 3/4
so we add that to the end since it will become 0 from derivitive

</span>
<span>f'(x)=3/4x^4+2x^3-1/2x^2+2x+4 and 3/4

now reverse drivitive again

3/4x^4
exponent is 5 and coefient is 3/4
5 times what=3/4? answer is 3/20
3/20x^5

2x^3
exponent should be 4 and coefient is 2
4 times what=2? answer is 1/2
1/2x^4

-1/2x^2
exponent should be 3 and coefient is -1/2
3 times what=-1/2? answer is -1/6
-1/6x^3

2x
exponent should be 2 and coefient is 2
2 times what=2? answer is 1
1x^2

4 and 3/4 turns to (4 and 3/4)x



</span>
<span>f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+(4 and 3/4)x
try evaluating it for x=1
f(1)=(3/20)+(10/20)-(10/50)+1+(19/4)
f(1)=6 and 7/30
what do we add to get -7
-13 and 7/30
</span>
<span><span>f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+(4 and 3/4)x-13 and 7/30

</span>


</span>ANSWER
<span>f'(x)=3/4x^4+2x^3-1/2x^2+2x+19/4
</span><span>f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+19/4x-187/30</span>
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