Questions from General Calculus

Q: Let s (t) be the distance (in feet)

Let s (t) be the distance (in feet) traveled by a parachutist after t seconds from the time of opening the chute, and suppose that s (t) has the line y = -15t + 10 as an asymptote. What does this impl...

Q: Let P(t) be the population of a bacteria culture

Let P(t) be the population of a bacteria culture after t days and suppose that P(t) has the line y = 25,000,000 as an asymptote. What does this imply about the size of the population?

Q: Sketch the graph of a function having the given properties.

Sketch the graph of a function having the given properties. Defined for 0 ≤ x ≤ 10; relative maximum point at x = 3; absolute maximum value at x = 10

Q: Sketch the graph of a function having the given properties.

Sketch the graph of a function having the given properties. Relative maximum points at x = 1 and x = 5; relative minimum point at x = 3; inflection points at x = 2 and x = 4

Q: Differentiate. y = √(1 + x2)

Differentiate. y = √(1 + x2)

Q: Sketch the graph of a function having the given properties.

Sketch the graph of a function having the given properties. Defined and increasing for all x Ú 0; inflection point at x = 5; asymptotic to the line y = (3/4)x + 5.

Q: Sketch the graph of a function having the given properties.

Sketch the graph of a function having the given properties. Defined for x ≥ 0; absolute minimum value at x = 0; relative maximum point at x = 4; asymptotic to the line y = (x/2) + 1

Q: Consider a smooth curve with no undefined points. (a

Consider a smooth curve with no undefined points. (a) If it has two relative maximum points, must it have a relative minimum point? (b) If it has two relative extreme points, must it have an inflectio...

Q: If the function f (x) has a relative minimum at

If the function f (x) has a relative minimum at x = a and a relative maximum at x = b, must f (a) be less than f (b)?

Q: Graph the function f (x) = 1 /

Graph the function f (x) = 1 / x3 - 2x2 + x - 2 in the window [0, 4] by [-15, 15]. For what value of x does f (x) have a vertical asymptote?