Find the critical numbers of the function g(t)=|5t-7|

Question

If you find g'(t) you just get 5 so would there be no critical numbers? Or am I missing something?

Answer 1

your graph consists of two straight lines
y = 5t-7 and y = -5t + 7 where you only want the part above the t-axis (x-axis normally)
The two lines meet on the t-axis at the point (7/5 , 0)

That point is called a "cusp" and it would be the only critical number.

Differentiating the function would be over-kill since when you find the derivative of a straight line, you just get the slope, which we knew already anyway.