Questions from General Calculus

Q: If f is a differentiable function and g (x) =

If f is a differentiable function and g (x) = x f (x), use the definition of a derivative to show that g'(x) = x f'(x) + f (x).

Q: If limx→a [f (x) + g (

If limx→a [f (x) + g (x)] = 2 and limx→a [f (x) - g (x)] = 1, find limx→a [f (x) g (x)].

Q: Estimate the value of f'(a) by zooming in on

Estimate the value of f'(a) by zooming in on the graph off. Then differentiate f to find the exact value of f'(a) and compare with your estimate. f (x) = 1/√x, a = 4

Q: Let P (x1, y1) be a point on the

Let P (x1, y1) be a point on the parabola y2 = 4px with focus F (p, 0). Let a be the angle between the parabola and the line segment FP, and let β be the angle between the horizontal line...

Q: (a). Sketch a curve whose slope is always positive and

(a). Sketch a curve whose slope is always positive and increasing. (b). Sketch a curve whose slope is always positive and decreasing. (c). Give equations for curves with these properties.

Q: The president announces that the national deficit is increasing, but at

The president announces that the national deficit is increasing, but at a decreasing rate. Interpret this statement in terms of a function and its derivatives.

Q: Sketch the graph of a function whose first and second derivatives are

Sketch the graph of a function whose first and second derivatives are always negative.

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

Sketch the graph of a function whose first derivative is always negative and whose second derivative is always positive.

Q: Sketch the graph of a function that satisfies all of the given

Sketch the graph of a function that satisfies all of the given conditions.

Q: Sketch the graph of a function that satisfies all of the given

Sketch the graph of a function that satisfies all of the given conditions.