Question

Find the slope of the tangent line to the curve at the given point. (Calculus II)

Answer 1

No, this is Calculus I, I'm pretty sure.

Answer 2

HOLD ON I AM STILL POSTING THE PHOTO. SMART ALLECKS.

Answer 3

The slope of the tangent line to \(f(x)\) at point \((x_0,y_0) \) is \(f'(x_0)\).

Answer 4

Okay, in this case \(y=f(x)\) I presume, and so \(f'(x) = dy/dx\).

Answer 5

\[
\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}
\]

Answer 6

And just as a note, the \[\frac{ dy }{ dx } = \frac{ 4 }{ 9 }\] is the answer to the problem.

Answer 7

\[
\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} =\frac{y'(t)}{x'(t)}
\]

Answer 8

Got it. Perfect. Thanks!

Answer 9

Remember that: \[
\frac{dy}{dt} = \frac{dy}{dx}\frac{dx}{dt}
\]We just use chain rule and solve for \(dy/dx\).