Find the slope-intercept equation of the tangent line to the graph of y=1/x^3 when x = ½.

Question

Find the slope-intercept equation of the tangent line to the graph of y=1/x^3  when x = ½.

hartnn · Answer

hi :)
what have you tried??

slope of tangent at a point = derivative of the equation at that point!

phi · Answer

$$ y = x^{-3} $$
find dy/dx and evaluate at x=1/2 to get the slope

then find the tangent point i.e. (x,y) on the curve y= x^-3  when x=1/2
you can write
$$ y - y_0 = m(x-x_0) $$
and then rewrite in the form
y = mx +b

anonymous · Answer

y = -48x+32? am I right? :) so sorry that i was unable to respond awhile ago my internet was malfunctioning :)))

anonymous · Answer

@hartnn @phi  yeah and my answer was incorrect at first because my derivative is incorrect. Thank you guys :)

anonymous · Answer

oh and i thought it was raised to -8 :)))

phi · Answer

Yes, looks good. Here is a plot