Question

It has been estimated that the number of Venutian Carp in the Tethis River is given by
V(t)= 3t^2+8t+203
Where t is the number of years since 1990
A.Evaluate V'(5)
B. Interpret what V'(5)means

Answer 1

What's stopping you?

Answer 2

what do you mean whats stopping me

Answer 3

Can't you do it on your own?

Answer 4

I am confussed on part A on where to begin

Answer 5

Do you know how to find \(V'(t)\)?

Answer 6

no

Answer 7

Well\[
V'(t) = \lim_{h\to 0}\frac{V(t+h)-V(t)}{h}\\
\]Which means:
\[\begin{split}
V'(5) &= \lim_{h\to 0}\frac{V(5+h)-V(5)}{h}\\

&=\lim_{h\to 0}\frac{3(5+h)^2+8(5+h)+203-[3(5)^2+8(5)+203]}{h}
\end{split}\]
Good luck =)

Answer 8

It would be really nice if you knew how to differentiate, wouldn't it?

Answer 9

yes

Answer 10

LOL wio giving first principle ><

Answer 11

Try to simplify that fraction a bit @farmergirl411

Answer 12

ok give me a minute

Answer 13

ok I got ((9h^2+168h+636/h))

Answer 14

is that right

Answer 15

No it is not.

Answer 16

what didi I do wrong

Answer 17

\[
\begin{split}
V'(5) &= \lim_{h\to 0}\frac{V(5+h)-V(5)}{h}\\
&=\lim_{h\to 0}\frac{3(5+h)^2+8(5+h)+203-[3(5)^2+8(5)+203]}{h}\\
&=\lim_{h\to 0}\frac{3(5+h)^2+8(5+h)-[3(5)^2+8(5)]}{h}\\
&=\lim_{h\to 0}\frac{3(5)^2+3(10h)+3(h)^2+8(5)+8h-[3(5)^2+8(5)]}{h}\\
&=\lim_{h\to 0}\frac{3(10h)+3(h)^2+8h}{h}\\
&=\lim_{h\to 0}\frac{30h+3h^2+8h}{h}\\
&=\lim_{h\to 0}30+3h+8\\
&=30+8\\
&=38
\end{split}
\]

Answer 18

I don't know where you went wrong, but wherever you didn't match me, you must have gone down the wrong path.

Answer 19

must be so then 38 is the anwer for part a

Answer 20

203−[3(5)2+8(5)+203] = -75-40 = -115

Answer 21

I am confussed who is right

Answer 22

im just showing u that u messed up the calculations for the constants

Answer 23

oh ok but so is the 38 right that wio got

Answer 24

6t+8= v'(5) = 38

Answer 25

yah

Answer 26

ok so you by any chance know how to do part b of this problem

Answer 27

you should practice simplying the first principle tho it usually cancels when you expand all the brackets!

Answer 28

ok

Answer 29

do you know how to do part b

Answer 30

Do you know that the first derivative gives you the slope or rate of change? In this case, the rate of change interpretation is more helpful. It tells you the rate of change in the number of carp