Questions from Calculus

Q: Describe how to find the slope of the tangent line to the

Describe how to find the slope of the tangent line to the graph of a function at a point.

Q: List four notation alternatives to f′(x).

List four notation alternatives to f′(x).

Q: Describe how to find the derivative of a function using the limit

Describe how to find the derivative of a function using the limit process.

Q: Describe the relationship between continuity and differentiability.

Describe the relationship between continuity and differentiability.

Q: Sketch a graph of a function whose derivative is always negative.

Sketch a graph of a function whose derivative is always negative. Explain how you found the answer.

Q: Sketch a graph of a function whose derivative is zero at exactly

Sketch a graph of a function whose derivative is zero at exactly two points. Explain how you found the answer.

Q: Do f and f′ always have the same domain? Explain

Do f and f′ always have the same domain? Explain.

Q: A function f is symmetric with respect to the origin. Is

A function f is symmetric with respect to the origin. Is f′ necessarily symmetric with respect to the origin? Explain.

Q: The tangent line to the graph of y = g(x

The tangent line to the graph of y = g(x) at the point (4, 5) passes through the point (7, 0). Find g(4) and g′(4).

Q: Find the slope of the tangent line to the graph of the

Find the slope of the tangent line to the graph of the function at the given point. f(x) = 3 − 5x, (-1, 8)