How would I find the slope of the graph for this problem? g(x)=(4)/(x-6) at the point (7,4).

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Answer 1 · 2018-01-15T17:31:38

derivative

for any curve slope of tangent is its derivative value at a particular point :)
so
#g^'(x) = (0 - 4*1)/(x-6)^2# = #-4/(x-6)^2#

now place x=7 ( as the derivative is dependent only upon #x# coordinate and not #y( or g(x) )# coordinate.

we get derivative value = -4
hence slope of the tangent is -4 at the point (7,4)

Hope u find it helpful :)

Answer 2 · 2018-01-15T18:37:43

#m=-4#

#•color(white)(x)m_(color(red)"tangent")=g'(x)" at x = 7"#

#g(x)=4/(x-6)=4(x-6)^(-1)#

#rArrg'(x)=-4(x-6)^-2=-4/(x-6)^2#

#rArrg'(7)=-4/1^2=-4#