Question

Let f : [0, 1] → R be a twice differentiable function in (0, 1) such that f(0) = 3 and f(1) = 5.
If the line y = 2 x + 3 intersects the graph of f at only two distinct points in (0, 1) then the least number of points x ∈ (0, 1) at which f ”(x) = 0, is ___________.

Answer 1

f' (a) = f' (b) = f' (c) = 2
⇒ f" (x) is zero
for atleast x1 ∈ (a, b) & x2 є (b, c)