Please help me with this AP Calculus question!!

9514 1404 393

  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

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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

yes

step-by-step explanation:

give me the question

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the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: