Question

1. If y=7x-x^3 and increases at the rate 4 units per second, how fast is the slope of the graph
changing when x = 3? [-72 units per second]​

Answer 1

$\huge{\fcolorbox{black}{grey}{\large{\fcolorbox{white}{black}{{\fcolorbox{grey}{purple}{❤AnSwEr❤}}}}}}$

Your answer is -48

Hello.  I hope this helps.

Explanation:

The slope at any point is given by the derivative

dy / dx = d ( 7x - x³ ) / dx = 7 - 3x²

How fast the slope is changing with respect to time

= the derivative of 7 - 3x² with respect to time

= d ( 7 - 3x² ) / dt

= d ( 7 - 3x² ) / dx   ×   dx / dt         (chain rule)

= -6x × dx/dt

We're given dx/dt = 4, and we're looking at x = 2, so the value is

-6 × 2 × 4

= -48