Find the equation of tangent line to the function y=-1/x^3 at the pointx=1.
The given function is:
We know that the first derivative of a function at any certain point (x,y) is equal to the slope of the tangent line.
Calculate the value of y for x=1:
After simplifying we get,
Let be m is the slope of the tangent line:
m= First derivative of y at (1,-1):
Find the first derivative of y:
Substitute the value of x=1 into the above expression:
We know that equation of a tangent line is:
Substitute the point (1, -1) and slope m=3 into Point-Slope Form:
After simplifying we get
The required equation of the tangent is:
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