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Find the point on the curve `y=x^3-11 x+5`at which the tangent is `y = x - 11`. |
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Answer» Equation of the tangent is , `y = x -11` Comparing it with `y = mx+c`, `m = 1` So, slope of the tangent is `1`. Now, equation of the curve is, `y = x^3-11x+5` `:. 1 = dy/dx = 3x^2-11` `=>3x^2 -11 = 1` `=>3x^2 = 12` `=>x^2 = 4` `=> x= +-2` When `x = 2, y = (2)^3-11(2)+5 = -9` If we put `x = 2, y = -9`, it satisfy the equation, `y = x-11`. So, it is the required point. When `x = -2, y = (-2)^3-11(-2)+5 = 19` If we put `x = -2, y = 19`, it does not satisfy the equation, `y = x-11`. So, the required point on the curve is `(2,-9)`. |
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