Continuous Calculus

Calculus Level 4

True or False?

Suppose ff is a real-valued continuous function defined on [0,1][0, 1] such that (2x1)(2f(x)x)>0(2x - 1)(2f(x) - x) > 0 for all x12.x \neq \frac 12.

If the first derivative f(12)f'\left(\frac 12 \right) exists, then f(12)f'\left(\frac 12 \right) cannot be smaller than 12\frac 12.

×

Problem Loading...

Note Loading...

Set Loading...