Unit 1-6A Exam Topics

Front

What does it mean if f '(3) = 0 and f"(3) < 0?

Back

There is a local maximum at x=3.

Front

What is the equation of the tangent line at x = 1 for f(x) = \sqrt{x}?

Back

y = \frac{1}{2}x + \frac{1}{2}

Front

If g''(3) = -8, what does this indicate about g(x) at x=3?

Back

g(x) is concave down at x=3.

Front

If f'(-3) = 5, what does this indicate about f(x) at x=-3?

Back

f(x) is increasing at x=-3.

Front

What is the definition of a local maximum?

Back

A point where the function value is higher than the values of the function at nearby points.

Front

What is the definition of a local minimum?

Back

A point where the function value is lower than the values of the function at nearby points.

Front

What does f'(x) > 0 indicate about the function f(x)?

Back

The function f(x) is increasing.

Front

What does f'(x) < 0 indicate about the function f(x)?

Back

The function f(x) is decreasing.

Front

What is the significance of f''(x) in determining concavity?

Back

If f''(x) > 0, the function is concave up; if f''(x) < 0, the function is concave down.

Front

What is the relationship between inflection points and concavity?

Back

An inflection point occurs where the concavity of the function changes.