Questions from General Calculus

Q: Find all points on the graph of the function f (x

Find all points on the graph of the function f (x) = 2 sin x sin2x at which the tangent line is horizontal.

Q: In this exercise we estimate the rate at which the total personal

In this exercise we estimate the rate at which the total personal income is rising in the Richmond-Petersburg, Virginia, metropolitan area. In 1999, the population of this area was 961,400, and the po...

Q: Show that the sum of the - and -intercepts of any

Show that the sum of the - and -intercepts of any tangent line to the curve √x + √y = √c is equal to c.

Q: If F (x) = f (g (x)),

If F (x) = f (g (x)), where f (-2)- 8, f'(-2) = 4, f'(5) = 3, g (5) = -2, and g'(5) = 6, find F'(5).

Q: If h (x) = √4 + 3f (x

If h (x) = √4 + 3f (x), where f (1) = 7 and f'(1) = 4, find h'(1).

Q: Find all points on the curve x2y2 + xy = 2 where

Find all points on the curve x2y2 + xy = 2 where the slope of the tangent line is -1.

Q: Find equations of both the tangent lines to the ellipse x2 +

Find equations of both the tangent lines to the ellipse x2 + 4y2 = 36 that pass through the point (12, 3).

Q: The Bessel function of order 0, y = j (x

The Bessel function of order 0, y = j (x), satisfies the differential equation xy" + y' + xy = 0 for all values of and its value at 0 is j (0) = 1. (a). Find j'(0). (b). Use implicit differentiation t...

Q: If f is the function whose graph is shown, let h

If f is the function whose graph is shown, let h (x) = f (f (x)) and g (x) = f (x2). Use the graph of f to estimate the value of each derivative. (a). h'(2) (b). g'(2)

Q: Use the table to estimate the value of h'(0,

Use the table to estimate the value of h'(0,5), where h (x) = f (g (x)).