Let f(x) = x5 + x2. The secant line between x = 0 and x = 1

Question:

Let f(x) = x5 + x2. The secant line between x = 0 and x = 1 has slope 2 (check this), so by the MVT, f′(c) = 2 for some c ∈ (0, 1). Plot f (x) 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 f. Zoom in on the point of tangency to estimate x-coordinate c of the point of tangency.