Questions from General Calculus

Q: Find the first and second derivatives of the function. Check to

Find the first and second derivatives of the function. Check to see that your answers are reasonable by comparing the graphs of f, f', and f". f (x) = ex - x3

Q: The equation of motion of a particle is s = t4 –

The equation of motion of a particle is s = t4 – 2t3 + t2 - t, where s is in meters and t is in seconds. (a). Find the velocity and acceleration as functions of t. (b). Find the acceleration after 1 s...

Q: If f (x) = 2x2 – x2, find f'

If f (x) = 2x2 – x2, find f'(x), f'''(x), f'''(x), and f4(x). Graph f, f', f'', and f" on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives?

Q: On what interval is the function f (x) = x3

On what interval is the function f (x) = x3 – 4x2 + 5x concave upward?

Q: Differentiate the function. f (t) = 2 –

Differentiate the function. f (t) = 2 – 2/3t

Q: Show that the function f (x) = |x –

Show that the function f (x) = |x – 6| is not differentiable at 6. Find a formula for f' and sketch its graph.

Q: Differentiate the function. g (t) = 2t-

Differentiate the function. g (t) = 2t-3/4

Q: Differentiate the function. h (t) = 4√

Differentiate the function. h (t) = 4√t – 4et

Q: The quantity of charge in Q coulombs (C) that has

The quantity of charge in Q coulombs (C) that has passed through a point in a wire up to time t (measured in seconds) is given by Q (t) = t3 – 2t2 + 6t + 2. Find the current when (a) t = 0.5s and (b)...

Q: Find an equation of the normal line to the parabola y =

Find an equation of the normal line to the parabola y = x2 – 5x + 4 that is parallel to the line x – 3y = 5.