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 given point. y = ln (x2 - 3x + 1), (3, 0)

Q: Show, using implicit differentiation, that any tangent line at a

Show, using implicit differentiation, that any tangent line at a point P to a circle with center O is perpendicular to the radius OP.

Q: The table shows how the average age of first marriage of Japanese

The table shows how the average age of first marriage of Japanese women varied in the last half of the 20th century. (a). Use a graphing calculator or computer to model these data with a fourth-degr...

Q: Find equations of the tangent lines to the curve y = (

Find equations of the tangent lines to the curve y = (lnx)/x at the points (1, 0) and (e, 1/e). Illustrate by graphing the curve and its tangent lines.

Q: (a). On what interval is f (x) =

(a). On what interval is f (x) = x ln x decreasing? (b). On what interval is f concave upward?

Q: The cost function for production of a commodity is C (x

The cost function for production of a commodity is C (x) = 339 + 25x – 0.09x2 + 0.0004x3 (a). Find and interpret C"(100). (b). Compare C"(100) with the cost of producing the 101st item.

Q: If p (x) is the total value of the production

If p (x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is A (x) = p (x)/x. (a). Find A'(x). Why does the company...

Q: Let f (x) = loga (3x2 – 2).

Let f (x) = loga (3x2 – 2). For what value of a is f'(1) = 3?

Q: The gas law for an ideal gas at absolute temperature T (

The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the...

Q: Differentiate the function. f (x) = ln (

Differentiate the function. f (x) = ln (sin2 x)