Question

given x= 2t^4 + 100^3 ,find dx/dt and find values of t when dx/dt =0

Answer 1

use power rule to find dx/dt

Answer 2

\[\large \frac{d}{dx}(x)^n = n \cdot (x)^{n-1}\]

Answer 3

in this case.....t

Answer 4

Put x = t...

Answer 5

But how do i find x

Answer 6

what do you mean find x?

Answer 7

you are going to find dx/dt not x..

Answer 8

I mean to say that first find dx/dt...

Answer 9

here's an example..

\[y = 3x^2 + 4x + 2\]
i want to find dy/dx
\[\frac{dy}{dx} = 6x + 4\]
now i want to find the value/s of x when dy/dx = 0
\[\implies 6x + 4 = 0\]
\[\implies 6x = -4\]
\[\implies x = -\frac 23\]
does that help?

Answer 10

Which would be 8t^3 +300t^2

Answer 11

\[\frac{dx}{dt} = 8t^3 + 300t^2\]
right..now solve for t when dx/dt = 0

Answer 12

\[\frac{\text d}{\text dt}(t)^n = n \cdot (t)^{n-1}\]
\[\frac{\text d}{\text dt}(2t^4 + 100t^3) = \frac{\text d}{\text dt}(2t^4)+ \frac{\text d}{\text dt}(100t^3)\]

Answer 13

Are you missing t there in your question ??

Answer 14

hmm? i thought you saw that coming?

Answer 15

Yes you are correct...

Answer 16

8t^3 +300t^2 \(\checkmark\)

Answer 17

@UnkleRhaukus \(\large \checkmark\)

Answer 18

@lgbasallote \(\sqrt{}\)

Answer 19

Ha ha ha ha...

Answer 20

Now equate what you have found to 0 and try to find values for t..

Answer 21

But how do i use dx/dt =0 and find value of t

Answer 22

\[\frac{\text dx}{\text dt}= 8t^3 +300t^2\]

\[0= 8t^3 +300t^2\]

Answer 23

hint: you're going to factor something out

Answer 24

And I don't think its \(t^4\)..

Ha ha ha..

Answer 25

Oh i get it thnx guys

Answer 26

aww i was ready for another example-slash-demo

Answer 27

what are the values for \(t\) ?

Answer 28

Dw i llbe posting alot of question which will make you scrach your head

Answer 29

i like scratches

Answer 30

scratch
and sniff?

Answer 31

And I like your spirit @lgbasallote