Find the point on the curve `y=x^3-11 x+5` at which the tangent is `y" "=" "x" "" "11` .

Explanation

Equation of curve
` y = x^(3) - 11x + 5` ….(1)
` rArr (dy)/(dx) =3x^(2) - 11`
Slope of tangent at point `(x, y) = 3x^(2) - 11`
Slope of tangent y = x - 11 is = 1
`:. 3x^(2) - 11 = 1`
` rArr x^(2) = 4`
`rArr x = 2 or x=-2`
put x = - 2 in equation (1)
`y= 2^(3) - 11 xx 2 + 5 =-9`
but the equation (1)
` y = (-2)^(3) - 11 xx (-2) + 5 = 19`
but the equation y = x - 11 is not satisfied by the point (-2, 19).
`:. ` Required point = (2, -9)