Questions from General Calculus


Q: Which one of the graphs in Fig. 18 could represent a

Which one of the graphs in Fig. 18 could represent a function f (x) for which f (a) = 0, f ‘(a) 0? Figure 18:

See Answer

Q: Sketch the graph of a function that has the properties described.

Sketch the graph of a function that has the properties described. f (2) = 1; f ‘(2) = 0; concave up for all x.

See Answer

Q: Sketch the graph of a function that has the properties described.

Sketch the graph of a function that has the properties described. f (-1) = 0; f ‘(x) 6 0 for x < -1, f ‘(-1) = 0 and f ‘(x) > 0 for x > -1.

See Answer

Q: Sketch the graph of a function that has the properties described.

Sketch the graph of a function that has the properties described. f (3) = 5; f (x) > 0 for x < 3, f ‘(3) = 0 and f (x) > 0 for x > 3.

See Answer

Q: Sketch the graph of a function that has the properties described.

Sketch the graph of a function that has the properties described. (-2, -1) and (2, 5) are on the graph; f ‘(-2) = 0 and f ‘(2) = 0; f ’’(x) > 0 for x < 0, f ’’(0) = 0, f ’’(x) < 0 for x > 0.

See Answer

Q: Sketch the graph of a function that has the properties described.

Sketch the graph of a function that has the properties described. (0, 6), (2, 3), and (4, 0) are on the graph; f ‘(0) = 0 and f ‘(4) = 0; f ’’(x) < 0 for x < 2, f ’’(2) = 0, f ’’(x) > 0 for x > 2.

See Answer

Q: Differentiate. y = 3√3 x

Differentiate. y = 3√3 x

See Answer

Q: Differentiate. y = 1 / 2x + 5

Differentiate. y = 1 / 2x + 5

See Answer

Q: Sketch the graph of a function that has the properties described.

Sketch the graph of a function that has the properties described. f (x) defined only for x ≥ 0; (0, 0) and (5, 6) are on the graph; f ‘(x) > 0 for x ≥ 0; f ’’(x) < 0 for x < 5, f ’’(5) = 0, f ’’(x) >...

See Answer

Q: Use the given information to make a good sketch of the function

Use the given information to make a good sketch of the function f (x) near x = 3. f (3) = 4, f ‘(3) = - 1/2, f ’’(3) = 5

See Answer