Answer:
so slope of the tangent line to the Curve at the point P = (1,1,5) is 9
Step-by-step explanation:
given:
z=x^4+5xy−y^4
so,
δz/δx = (4x^3+5y-0)
(δz/δx)_(1,1) = m = 4(1)^3 +5(1)
= 9
so slope of the tangent line to the Curve at the point P = (1,1,5) is 9
The slope of the tangent line of this curve at point P is 9.
Since The plane y=1 intersects the surface [tex]z=x^4+5xy-y^4[/tex] in a certain curve.
And, there is the point P=(1,1,5)
So if we can take the value of x be 1 so we can determine the slope
So,
[tex]= 4(1)^3 +5(1)[/tex]
= 9
Hence, The slope of the tangent line of this curve at point P is 9.
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