The number of continuous and derivable functions such that and for all is/are

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The number of continuous and derivable functions

f(x)

such that

f(1) = -1, f(4) = 7

and

f'(x) > 3

for all

x \in R

is/are (a) 0 (b) 1 (c) 3 (d) infinite