Transpose formula to find a value

Question

Can someone help with this please?

Ive differentiated a formula to get a value, now I need to find the positive value for t for when $\frac{dR}{dt} = 0$

So:

$0 = (27t^{0.5} e^{-3t}) + (-54t^{1.5} e^{-3t})$

How would go about finding t here?

score 2 · Accepted Answer · answered Nov 10 '17 at 20:50

2

Factor: $$0 = (27t^{0.5} e^{-3t}) + (-54t^{1.5} e^{-3t}) =27\sqrt{t}e^{-3t}\left(1-2t\right) $$ so $t=0$ or $t=1/2$. If you are looking for strictly positive values then $t=1/2$.

answered Nov 10 '17 at 20:50

Malcolm

1,055

That's the answer I was looking for 0.5, can you explain what you did there please? I dont see where the (1-2t) came from – PMA Nov 10 '17 at 20:53
1

Ahh i see it, so then you solve for each of the factors to get two different answers... Thanks! – PMA Nov 10 '17 at 20:56

score 1 · Answer 2 · answered Nov 10 '17 at 20:30

1

You can divide out $27t^{0.5}e^{-3t}$ and be left with a linear equation.

answered Nov 10 '17 at 20:30

Ross Millikan

374,822

Would that leave, $0 = -54t^{1.5} e^{-3t} + 1$? – PMA Nov 10 '17 at 20:35

Transpose formula to find a value

2 Answers2