Let for and let

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

Problem

Let

f(x)=x^{2}+1

for

x\in[1,4]

and let

g_k(x)=k x

, where

k

is a real parameter. For which values of

k

is there at least one number

c

[1,4]

such that

f(c)=g_k(c)

? (a)

k\ge 2

(b)

k\in(2,\,\dfrac{17}{4})

(c)

k\in[2,\,\dfrac{17}{4}]

(d)

k\in[2,\,4]