Question

Find an equation of the line tangent to the graph of x^2+(y-x)^3=9 at x=1

Answer 1

x^2+(y-x)^3=9
at x=1, y=3

2x + 3(x-y)^2 (y' - 1) = 0
y' = 1 - 2x/(3(y-x)^2)
at (1,3) y' = 1 - 2/12 = 5/6

so the tangent line is y-3 = 5/6 (x-1)

Answer 2

you can see that graphs at

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Answer 3

Thank you

Answer 4

self