Main content

Differential Calculus

Course: Differential Calculus > Unit 1

Lesson 16: Intermediate value theorem

Justification with the intermediate value theorem

The table gives selected values of the continuous function f.

x	minus, 3	0	5	17
f, left parenthesis, x, right parenthesis	110	230	175	45

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.

(Choice A)
Yes, Isla's justification is complete.
(Choice B)
No, Isla didn't establish that 200 is between f, left parenthesis, 0, right parenthesis and f, left parenthesis, 5, right parenthesis.
(Choice C)
No, Isla should've mentioned that f is continuous.

Stuck?

Differential Calculus

Course: Differential Calculus > Unit 1

Problem