Question

Suppose y = 2x + 1 where x and y are functions of t.
(a) If dx/dt = 6, find dy/dt when x = 4.
(b) If dy/dt = 4, find dx/dt when x = 40.

Answer 1

Can you do implicit differentiation?

Answer 2

\[
y = 2x + 1 \\
\frac{dy}{dt} = 2\frac{dx}{dt} + 0 \\
a) \frac{dx}{dt} = 6. ~~\text{Sub above and find }\frac{dy}{dt}
\]

Answer 3

so then its 12?

Answer 4

my online hw is saying thats the wrong answer

Answer 5

with implicit diff. ...which is sad that I have to review at my level in Calculus

Answer 6

http://dufu.math.ncu.edu.tw/calculus/calculus_bus/img539.gif

Answer 7

\[
y = 2x + 1 \\
\frac{dy}{dx} = 2 = \large \frac{\frac{dy}{dt}}{\frac{dx}{dt}}\\
\frac{dy}{dt} = 2\frac{dx}{dt} \\
a) \frac{dx}{dt} = 6 \\
\frac{dy}{dt} = 2 * 6 = 12 \\
b) \frac{dy}{dt} = 4 \\
\frac{dx}{dt} = 4/2 = 2 \\
\]IDK why it is saying it is wrong.

Answer 8

By any chance is \(\large y = 2^x + 1\) instead of \(\large y = 2x +1 \) ?