Shown here is the graph of y = h(x) a) State the domain and range of h. b) Find

Question

Shown here is the graph of y = h(x) a) State the domain and range of h. b) Find the following limits (if they exist): lim x tends to 2 h(x) = lim x tens to -1 h(x) = c) Find the average rate of-change of is on [-5, -2]. d) List any x -values at Which h is not differentiable and describe the type of behavior at those points. 7) The next statements are false. Explain why or give a counterexample. (5 pt cat a) If f is continuous at x = a, then f is differentiable at x = a. b) If f(3) 8, there must be an x -value k between 3 and 4 for which f(k) = 8 8) Find all values of a such that the lines tangent to y = x^3 ? 4x and y = 1/x at x = a are parallel. BONUSES (must show correct work justifying your answer in order to get credit) B1) Find lim p tends to 5 fourth root p ? fourth root 5/ p-5 B2) Let f(x) =

Explanation / Answer

a) Domain [-6,infinity)

Range (-2,infinity)

b) Both limits does not exist

c) -2/3

d) x=-4,-1,2

7 a) false. eg f(x) = |X|

b) False, only for continuous curves this is true.

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8) Tangents are parallel implies derivatives are equal

3x-4 = -1/x2

3x3-4x2+1 =0

x =1 or x = 1/3

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B1)4(5)1/3

B2) 0

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