a) True or False: If f[x] is a positive function, then the instantaneous percent

Question

a) True or False: If f[x] is a positive function, then the instantaneous percentage growth rate of h[x] = k f[x] is exactly the same as the instantaneous percentage growth rate of f[x] .

b) ?True or False: If f[x] and g[x] are positive functions, then the instantaneous percentage growth rate of f[x] + g[x] is exactly the same as the instantaneous percentage growth rate of f[x] plus the instantaneous percentage growth rate of g[x] .?

c)?True or False: If f[x] and g[x] are positive functions, then the instantaneous percentage growth rate of h[x] = f[x] g[x] is exactly the same as the instantaneous percentage growth rate of f[x] plus the instantaneous percentage growth rate of g[x] .?

d) True or False: If f[x] and g[x] are positive functions, then the instantaneous percentage growth rate of h[x] = f[x]/g[x] is exactly the same as the instantaneous percentage growth rate of f[x] minus the instantaneous percentage growth rate of g[x].

e) True or False: If f[x] is a positive function, then the instantaneous percentage growth rate of h[x] = k f[x]^2 is exactly the same as twice the instantaneous percentage growth rate of f[x].

f) ?True or False: If f[x] is a positive function, then the instantaneous percentage growth rate of h[x] = k f[x]^r is exactly the same as r times the instantaneous percentage growth rate of f[x].

Explanation / Answer

The rate of change at a particular moment. Same as the value of the derivative at a particular point. For a function, the instantaneous rate of change at a point is the same as the slope of the tangent line. That is, it's the slope of a curve.

So for this problem the rules which are applicable to derivatives will be applied here.

1. False. the instantaneous percentage growth rate of h[x] = k f[x] is exactly the same as the instantaneous percentage growth rate of f[x] multiplied by k.

b. True.

C.false

D.false

E.true

F. True

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