Because the derivative of a function represents both the slope of the tangent to

Question

Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. Consider the graph of the function

y = f(x)

given in the figure.

(a) Over what interval(s) (a) through (d) is the rate of change of f(x) positive? (Select all that apply.)

a b c d

(b) Over what interval(s) (a) through (d) is the rate of change of f(x) negative? (Select all that apply.)

a b c d

(c) At what point(s) A through E is the rate of change of f(x) equal to zero? (Select all that apply.)

A B C D E

Explanation / Answer

Part (a):

The rate of change of f(x) is positive in the interval where the solpe of the function is positive.

Therefore the intervals are: a, b and d

Part (b):

The rate of change of f(x) is negative in the interval where the solpe of the function is negative.

Therefore the interval is: c

Part (c):

The rate of change of f(x) is equal to zero is the critical point.

Therefore the points are: A, C and E. Ans

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