Question

PLEASE HELP!

Answer 1

Both the first and second statements are true and therefore Option D is the correct answer .

What is a Function ?

A function can be defined as the equation that identifies relation between a dependent variable and an independent variable.

A function always has a defined range and domain.

In the following statements

I. If f '(c) = 0, then f has a local maximum or minimum at x = c.

f'(c) = 0

It means that the slope of f(x) = 0 at x = c

If f has a local maximum or minimum at x = c  It is a True statement

II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].

If f'(x) = 0 on (a, b),

then f is neither increasing nor decreasing

and therefore is constant on [a, b]

So it is a True statement.

III. The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [−1, 1].

No the theorem cannot be applied as, f is neither continuous nor differentiable at x = 0

It is a False Statement.

Therefore Option D is the correct answer.

To know more about Function

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