Mathematics

Mathematics

Problem

For a real parameter

a

, consider the functions

f(x)=e^{x}

and

g_a(x)=ax+2

on the closed interval

[0,2]

. a. Write an explicit expression for

h_a(x)=f(x)-g_a(x)

. b. Compute

h_a(0)

and

h_a(2)

in terms of

a

. State the sign of each value when

a=1

,

a=3

, and

a=5

. c. Determine all real values of

a

for which the equation

e^{x}=ax+2

has at least one solution

x

in the interval

(0,2)

. Justify your answer thoroughly.

Browse the problem library