- #1

member 731016

- Homework Statement
- Please see below

- Relevant Equations
- Please see below

For this problem,

I'm confused by the implication from the antecedent ##0 < |x - c| < \delta## to the consequent. Should the consequent not be ##|f''(x) - f''(c)| < \frac{1}{2}## where ##\epsilon = \frac{1}{2}## (Since we are applying the definition of a limit for the first derivative curve)?

##|f''(x) - f''(c)| < \frac{1}{2}##

##\leftrightarrow |f''(x) - \frac{f'(x) - f'(c)}{x - c}| < \frac{1}{2}##

##\leftrightarrow |f''(x) - 1| < \frac{1}{2}##

I don't understand why they don't have ##f''(x)## in their expression. Does someone please know why?

Thanks!

I'm confused by the implication from the antecedent ##0 < |x - c| < \delta## to the consequent. Should the consequent not be ##|f''(x) - f''(c)| < \frac{1}{2}## where ##\epsilon = \frac{1}{2}## (Since we are applying the definition of a limit for the first derivative curve)?

##|f''(x) - f''(c)| < \frac{1}{2}##

##\leftrightarrow |f''(x) - \frac{f'(x) - f'(c)}{x - c}| < \frac{1}{2}##

##\leftrightarrow |f''(x) - 1| < \frac{1}{2}##

I don't understand why they don't have ##f''(x)## in their expression. Does someone please know why?

Thanks!