Why is the inverse of a gradient -1/x?
Because the value, x and its inverse, -1/x should multiply together to give -1. This is proof that two lines are perpendicular (or having the same magnitude of gradient but opposite signs +/- ).
SR
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Find the equation of the tangent to the curve x^3+yx^2=1 at the point (1,0).
I don't fully understand the purpose of integration. Could you please explain it to me?
integrate by parts the equation dy/dx = (3x-4)(2x^2+5).