Question

find the slope of tangentg line at x(1/x2 - 1/4) when x=-2

Answer 1

is your function\[f(x) = \frac{ 1 }{ x }-\frac{ x }{ 4 }\]?

Answer 2

When I distribute the x through the first equation I get:

y=1/x - x/4

so y'= 1/x^-2 - 1/4

Plugging in x= -2 I get y'(-2) = -1/2 (this is the slope of the tangent line)

In order to find the equation of the tangent line Plugging in x= -2 in the first equation I get y = 0

Using the Point-Slope formula:

y-0 = -1/2(x-(-2))

So the equation of the tangent line is y = -1/2x - 1

Answer 3

your y' is off by a little bit.
you have y = x^(-1) - x/4
y' = -x^(-2) - 1/4
Try recalculating your slope based on this

Answer 4

@jollyjolly0 thanks

@jonathan1992v

y' is infact -x^(-2) - 1/4 but I just forgot include the (-) sign, but in my calculations I included it, so the slope stays the same.