Mathematics

Problem

Consider the continuous function

R(x)=e^{x}-2x^{2}+3

defined for all real

x

. a. Verify that

R(-2)

and

R(0)

have opposite signs, and use this fact to justify the existence of a real number

c_1

with

-2<c_1<0

such that

R(c_1)=0

. State the numerical values you compute for

R(-2)

and

R(0)

.},{