What the slope of #x^4y^4=16# at #(2,1) #?
1 Answer
May 13, 2018
The slope (of the tangent) to the curve at the given coordinate is
Explanation:
We seek the slope (of the tangent) to the curve:
# x^4y^4 = 16 #
at the coordinate
The gradient of the tangent to a curve at any particular point is given by the derivative of the curve at that point. So if we differentiate the equation implicitly, and apply the product rule, then we have:
# (x^4)(d/dx y^4) + (d/dx x^4)(y^4) = 0 #
# :. (x^4)(4y^3 dy/dx) + (4x^3)(y^4) = 0 #
So if the slope of the tangent at the given coordinate
# :. (2^4)(4*1^3 *m) + (4*2^3)(1^4) = 0 #
# :. 16(4m) + 4*8 = 0 #
# :. 2m + 1 = 0 #
# :. m =-1/2 #
