Unit5 Test 5.1-5.4

Front

What does it indicate when f'(x) changes from positive to negative?

Back

There is a maximum.

Front

What does MVT stand for in calculus?

Back

Mean Value Theorem.

Front

What does it indicate when f'(x) changes from negative to positive?

Back

There is a minimum.

Front

What condition must f' satisfy for f to have a relative extrema?

Back

f' changes sign.

Front

How do you find the critical points of a function?

Back

Set f'(x) = 0 and solve for x.

Front

What is the significance of critical points in calculus?

Back

They are potential locations for relative maxima and minima.

Front

What is the definition of a relative maximum?

Back

A point where the function value is higher than its neighboring values.

Front

What is the definition of a relative minimum?

Back

A point where the function value is lower than its neighboring values.

Front

What is the relationship between the first derivative and the slope of a function?

Back

The first derivative indicates the slope of the tangent line to the function.

Front

What does it mean if f'(x) = 0 at a point?

Back

The function has a horizontal tangent line at that point.