Consider the discretion, Derivatives question

Question

h(x) = f(x)/(2-f(x))

below is a table of values with f'(x) being the derivative of f(x)

l x l f(x) l f'(x)l

l 1 l 3 l 2 l

l 3 l -5 l 7 l

a) Determine the equation of the tangent line to the graph of f(x) at x = 1

b) Is f(x) continuous at x = 2? Justify your response.

c) Use the intermediate value theorem to justify the existence of a zero on the interval [1, 3].

d) Determine h'(3)

Answer 1