Question

All polynomial functions are continuous over all real numbers

true of false

rational functions are discontinuous where the numerator is equal to zero

true or false

exponential functions are continuous over all real numbers

true or false

log functions are continuous over all real numbers

true or false

The first derivative of a function gives the average rate of change at a point

true or false

The second derivative of a function gives the instantaneous rate of change at a point

true or false

if the first derivative of a function changes sign when X=7 and the second derivative of that function is positive at X=7, there will be a minimum point at X=7

true or false

Answer 1

1. All polynomial functions are continuous over all real numbers.....TRUE

2. rational functions are discontinuous where the numerator is equal to zero.....FALSE

(note: rational functions are discontinuous where denominator becomes zero)

3. exponential functions are continuous over all real numbers.......TRUE

4. log functions are continuous over all real numbers......FALSE

(note: not continuous at the point zero)

5. The first derivative of a function gives the average rate of change at a point....FALSE

(note: it gives the instantaneous rate of change)

6. The second derivative of a function gives the instantaneous rate of change at a point.....FALSE

(note: it is actually the rate of rate of change of the function!)

7. if the first derivative of a function changes sign when X=7 and the second derivative of that function is positive at X=7, there will be a minimum point at X=7......TRUE