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Carl_M
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hints? Derivatives: Intervals, stationary points, logarithms, continuous functions
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 modeled 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) ?
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 modeled 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) ?