Questions from General Calculus

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the point corresponding to the given value of the parameter.

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the point corresponding to the given value of the parameter.

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the point corresponding to the given value of the parameter.

Q: Coffee is being poured into the mug shown in the figure at

Coffee is being poured into the mug shown in the figure at a constant rate (measured in volume per unit time). Sketch a rough graph of the depth of the coffee in the mug as a function of time. Account...

Q: Find the points on the curve where the tangent is horizontal or

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work.

Q: Find the points on the curve where the tangent is horizontal or

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work.

Q: The equation of motion of a particle is s = t3 –

The equation of motion of a particle is s = t3 – 3t, where s is in meters and is in seconds. Find (a). the velocity and acceleration as functions of t, (b). the acceleration after 2 s, and (c). the ac...

Q: A curve C is defined by the parametric equations x = t2

A curve C is defined by the parametric equations x = t2, y = t3 – 3t. (a). Show that C has two tangents at the point (3, 0) and find their equations. (b). Find the points on C where the tangent is hor...

Q: For what values of does the graph of f (x)

For what values of does the graph of f (x) = x3 + 3x2 + x + 3 have a horizontal tangent?

Q: Show that the curve y = 6x3 + 5x - 3 has

Show that the curve y = 6x3 + 5x - 3 has no tangent line with slope 4.