- #1

Carl_M

- 13

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**hints??? Derivatives: Intervals, stationary points, logarithms, continuous functions**

## Homework Statement

Got any hints or anything?

1. Suppose that f(x) = (x - 3)^4 ( 2x + 5)^5

a) Find and simplify f ' ( x )

b) Find stationary points of f

c) Find exactly the intervals where f is increasing and intervals where f is decreasing

2. Find the stationary points of g(x) = 2cos - sqrt(3)x , 0< _ x < _ 2pi and classify them (as local minimum, local maximum or neither).

3. The temperature of the ground at a distance of d centimetres below the surface at a certain location can be modelled by g(t) = 16t + 11e^-0.00706dCOS(2(pi)(t) - 0.00706d-0.628)

where t is the time in years since July 1.

a) Find and interpret g(t) and g '(t) on sept 1 at ground level (d =0)

b) Find and interpret g(t) and g '(t) on sept 1 at 3 m below ground level.

4. Let h be continuous, differentiable function such that g(3) = -7, g(-7) = 3, g '(3) = 2, and g '(-7) = 4

a) Find (g^-1)(3) and (g^-1) '(3)

b) Find an equation for the tangent line to the graph of g^-1(x) at x=3

c) With only the information, what is your best estimate of (g^-1)(4) ?