Questions from General Calculus

Q: Differentiate each trigonometric identity to obtain a new (or familiar)

Differentiate each trigonometric identity to obtain a new (or familiar) identity.

Q: Find the points on the curve y = 2x3 + 3x2 –

Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent is horizontal.

Q: Differentiate. y = sec θ tan θ

Differentiate. y = sec θ tan θ

Q: (a). If g (x) = x2/3

(a). If g (x) = x2/3, show that g'(0) does not exist. (b). If a ≠ 0, find g'(a). (c). Show that y = x2/3 has a vertical tangent line at (0, 0). (d). Illustrate part (c) by graphing y = x2/3.

Q: On what interval is the function f (x) = x3ex

On what interval is the function f (x) = x3ex increasing?

Q: On what interval is the function f (x) = x2ex

On what interval is the function f (x) = x2ex concave downward?

Q: How many tangent lines to the curve y = x/ (

How many tangent lines to the curve y = x/ (x + 1) pass through the point (1, 2)? At which points do these tangent lines touch the curve?

Q: At what point on the curve y = 1 + 2ex –

At what point on the curve y = 1 + 2ex – 3x is the tangent line parallel to the line 3x – y = 5? Illustrate by graphing the curve and both lines.

Q: Use the method of Exercise 55 to compute Q'(0),

Use the method of Exercise 55 to compute Q'(0), where Q (x) = 1 + x + x2 + xex/ 1 – x + x2 - xex Exercise 55: Find R'(0), R(x) = x + 3x3 + 5x5/1 + 3x3 + 6x6 + 9x9 where Hint: Instead of finding R’(x...

Q: The cost, in dollars, of producing yards of a certain

The cost, in dollars, of producing yards of a certain fabric is C (x) = 1200 + 12x – 0.1x2 + 0.0005x3 (a). Find the marginal cost function. (b). Find C"(200) and explain its meaning. What does it pred...