6) Can we apply the Intermediate value Theorem?

a) Suppose ?(?) is continuous over the interval [4, 8] with ?(4)=?1 and ?(8)=5, is the following statement correct? Explain

It is always true that ?(?)=0 for some z in the interval [4, 8].

b) Suppose ?(?)=1? with ?(?1)=?1,?(1)=1, is the following statement true or not? Explain.

According to Intermediate value Theorem ?(?)=0 for some z in the interval [-1, 1].

c) Suppose ?(?) is continuous for all x with ?(?1)>0,?(1)>0, is the following statement true? Explain.

According to Intermediate Value Theorem ?(?)=0 for some z in the interval [-1, 1].

7) Use Intermediate theorem to check that a zero exists for f(x) in the interval [0,1], then use Desmos or graphing calculator to find the zero round to two decimal places. ?) ?(?)=?+???3

Explain why there is a zero between [0, 1]:

What is the zero?

b) ?(?)=?4??2+3??1

Explain why there is a zero between [0, 1]:

What is the zero?

6) Can we apply the Intermediate value Theorem? a) Suppose f (x) is continuous over the interval [4, 8] with f (4) = 1 and f(8) = 5. is the following statement correct? Explain It is always true that f (z) = 0 for some 2 in the interval [4. 8]. b) Suppose f (x) = i with f(1) = 1, f (1) = 1. is the following statement true or not? Explain. According to Intermediate value Theorem f (z) = 0 for some 2 in the interval [-1, 1]. c) Suppose f(x) is continuous for all x with f( 1) > 0, f (1) > 0, is the following statement true? Explain. According to Intermediate Value Theorem f (z) = 0 for some 2 in the interval [-1. 1]. 7) Use Intermediate theorem to check that a zero exists for x) in the interval [0.1]. then use Desmos or graphing calculator to nd the zero round to two decimal places. a)f(x)=x+e"3 Explain why there is a zero between [0. 1]: What is the zero? b) f(x)=x4-x2+3x1 Explain why there is a zero between [0. 1]: What is the zero