Question

Find the derivative of f(x) = negative 9 divided by x at x = 6.

Answer 1

First, find f(x+h) = (-9/(x+h)) ... just substitue (x+h) for every x.

Then plug in f(x+h) and f(x) in the difference quotient formula.

Lim/h->0\ [f(x+h) - f(x)]/h

Or, [(-9/ (x+h)) - -9/x] /h
Or, [(-9/ (x+h)) + 9/x]/h
Or, [(-9x + 9x + 9h)/ x(x+h)] / h
Or, [9h / (x^2 + hx)]/h .............................................. add like terms
Or, ( 9h / (x^2 + hx)) * h/1 .................divide by 7 is equivalent to multiply by 1/7
Or, 9/ (x^2 + hx) .................................cancle out the h
Or, 9/ x^2 ........................................... plug in 0 for h

Now, the function asks for x=6, so we plug in 6 for every x
so, the limit = 9/ 6^2 = 9/36 = 1/4.

Answer 2

F(x) = -9/x f(6) = -9/6 f(6) = -3/2 f(6) = -1.5 The function of f(x) = -9 / x at x = 6 is equal to -3 / 2 or -1.5. Hope that helps!