Question

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of "c" guaranteed by the theorem.

f(x)=(x^2) + x - 1, [0,5] f(c) =11

Answer 1

do you just plug in 11?

Answer 2

well you first show that 11 is between f(0) and f(5)
then in order to find c
you solve:
11 = c^2 +c - 1

Answer 3

how do you show that 11 is between f(0) and f(5)?

Answer 4

what is f(0) ?

Answer 5

do you just plug in 0 to the equation?

Answer 6

yes

Answer 7

f(0) = -1

Answer 8

good and f(5) ?

Answer 9

29

Answer 10

so 11 is really between them
and according to the theorem there must be a value for c such that f(c) = 11

Answer 11

now find c
11=c^2 + c - 1

Answer 12

do I add over the 1 or subtract the 11?

Answer 13

@Coolsector

Answer 14

you better subtract the 11
so you will get quadratic equation

Answer 15

(x+4)(x-3)=0

Answer 16

but the answer in my book says f(3)=11, why not use f(-4) ?

Answer 17

because the interval was [0,5]

Answer 18

OH. wow okay LOL thank you

Answer 19

yw:)