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. In Problems 31 and 32, use the graph of the function y = f ( x ) given in Figure 9.26. (a) Over what interval(s) ( a ) through ( d ) is the rate of change of f(x) positive? (b) Over what interval(s) (a) through ( d) is the rate of change of f ( x) negative? (c) At what point(s) A through E is the rate of change of f(x) equal to zero?
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. In Problems 31 and 32, use the graph of the function y = f ( x ) given in Figure 9.26. (a) Over what interval(s) ( a ) through ( d ) is the rate of change of f(x) positive? (b) Over what interval(s) (a) through ( d) is the rate of change of f ( x) negative? (c) At what point(s) A through E is the rate of change of f(x) equal to zero?
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. In Problems 31 and 32, use the graph of the function
y
=
f
(
x
)
given in Figure 9.26.
(a) Over what interval(s) (a) through (d) is the rate of change of f(x) positive?
(b) Over what interval(s) (a) through (d) is the rate of change of f(x) negative?
(c) At what point(s) A through E is the rate of change of f(x) equal to zero?
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