Using the Lagrange’s mean value theorem determine the values of x at which the tangent is parallel to the secant line at the e

Using the Lagrange’s mean value theorem determine the values of x at which the tangent is parallel to the secant line at the end points of the given interval:

(i) f(x) = x³ – 3x + 2, x ∈ [-2, 2]

(ii) f(x) = (x – 2)(x – 7), x ∈ [3, 11]

Using the Lagrange’s mean value theorem determine the values of x at which the tangent is parallel to the secant line at the end points

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