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Find the points on the curve `y=x^3`at whichthe slope of the tangent is equal to the `y `coordinate of the point. |
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Answer» Equation of curve `y = x^(3)` …(1) ` rArr (dy)/(dx) = 3x^(2)` Slope of tangent at point `(x, y) = 3x^(2)` Given ` 3x^(2) = y` ` rArr 3x^(2) = x^(3)` From equation (1) ` rArr x^(2) (3-x)=0` ` rArr x = 0 or x= 3` put x = 0 in equation (1) we get y = 0 put x = 3 in equation (1) we get ` y=3^(3) = 27` `:. ` Required point = (0, 0) or (3, 27) . |
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