Consider f over 3 10 find the value of c guaranted by the

Question

Consider the function f (x) = (x - 2)^2/3 = (³√(x -2))² shown, with f' (x) = (2/3) (x - 2)^-1/3 = 2 / 3 ³√(x - 2).

a. Circle all intervals below over which the hypothesis of the EVT is met.

[1, 10]       [2, 10]

b. Circle all intervals below over which the hypothesis of the MVT is met.

[1, 10]        [2, 10]

c. Consider f over [3, 10]. Find the value of c guaranted by the conclusion of the MVT. Draw the secant line through (3, f(3)) and (10, f(10)), and then the tangent line at (c, f(c)).