Let (x) = x 5 + x 2 . The secant line between (0, 0) and (1, 2) has slope 2 (check this), so by

Let ƒ(x) = x⁵ + x². The secant line between (0, 0) and (1, 2) has slope 2 (check this), so by the MVT, ƒ'(c) = 2 for some c ∈ (0, 1). Plot f and the secant line on the same axes. Then plot y = 2x + b for different values of b until the line becomes tangent to the graph of ƒ. Zoom in on the point of tangency to estimate the x-coordinate c of the point of tangency.