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## Differential Calculus

### Course: Differential Calculus>Unit 1

Lesson 16: Intermediate value theorem

# Justification with the intermediate value theorem

## Problem

The table gives selected values of the continuous function f.
xminus, 30517
f, left parenthesis, x, right parenthesis11023017545
Below is Isla's attempt to write a formal justification for the fact that the equation f, left parenthesis, x, right parenthesis, equals, 200 has a solution where 0, is less than or equal to, x, is less than or equal to, 5.
Is Isla's justification complete? If not, why?
Isla's justification:
We are given that f is continuous.
So, according to the intermediate value theorem, f, left parenthesis, x, right parenthesis, equals, 200 must have a solution when x is between x, equals, 0 and x, equals, 5.