009A Sample Midterm 2, Problem 2

The function $f(x)=3x^{7}-8x+2$ is a polynomial and therefore continuous everywhere.

a) State the Intermediate Value Theorem.

b) Use the Intermediate Value Theorem to show that $f(x)$ has a zero in the interval $[0,1].$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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