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3 years ago

Please help me with this AP Calculus question!!

Mathematics

1 answer:

Temka [501]3 years ago

7 0

9514 1404 393

Answer:

B. 3

Step-by-step explanation:

If all you want is a numerical result, sometimes a graphing calculator can provide that easily. The attachment shows it calculates the slope at x=4 to be 3.

dy/dx = 3 at x = 4

The derivative of the expression can be found from the quotient formula:

d(u/v) = (du·v -u·dv)/v²

y' = ((x -2)(2x -7) -(x^2 -7x +2)(1))/(x -2)^2

= (2x^2 -11x +14 -x^2 +7x -2)/(x -2)^2

= (x^2 -4x +12)/(x -2)^2

= ((x -4)x +12)/(x -2)^2

Then for x=4, we have ...

y' = 12/4 = 3

dy/dx = 3 at x = 4

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