Questions from General Calculus

Q: Find f"(x) and f"(x). f

Find f"(x) and f"(x). f (x) = x2 / 1 + 2x

Q: Find f"(x) and f"(x). f

Find f"(x) and f"(x). f (x) = x/x2 - 1

Q: Let f (x) = (x – 1)2

Let f (x) = (x – 1)2 g (x) = e-2x and h (x) = 1 + ln (1 – 2x) (a). Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened? (b). Graph f, g, and h and the...

Q: Find an equation of the tangent line to the given curve at

Find an equation of the tangent line to the given curve at the specified point. y = 2x/x + 1, (1, 1)

Q: Differentiate. f (x) = (x3 + 2x

Differentiate. f (x) = (x3 + 2x) ex

Q: Find an equation of the tangent line to the given curve at

Find an equation of the tangent line to the given curve at the specified point. y = ex/x, (1, e)

Q: Find equations of the tangent line and normal line to the given

Find equations of the tangent line and normal line to the given curve at the specified point. y = √x/ x + 1, (4, 0.4)

Q: (a). The curve y = 1/ (1 +

(a). The curve y = 1/ (1 + x2) is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point (-1, 1/2). (b). Illustrate part (a) by graphing the curve and the tang...

Q: (a). If f (x) = (x3 –

(a). If f (x) = (x3 – x) ex, find f'(x). (b). Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f'.

Q: The graph of f is given. State, with reasons,

The graph of f is given. State, with reasons, the numbers at which f is not differentiable.