For Exercises 95—96, find the average rate of change on the given interval. Give theexact value and an approximation to 4 decimal places. Verify that your results arereasonable by comparing the results to the slopes of the lines given in the graph. 95. f ( x ) = sin x a. [ 0 , π 6 ] b. [ π 6 , π 3 ] c. [ π 3 , π 2 ]
For Exercises 95—96, find the average rate of change on the given interval. Give theexact value and an approximation to 4 decimal places. Verify that your results arereasonable by comparing the results to the slopes of the lines given in the graph. 95. f ( x ) = sin x a. [ 0 , π 6 ] b. [ π 6 , π 3 ] c. [ π 3 , π 2 ]
Solution Summary: The author calculates the average rate of change of f(x)=sinx on the interval
For Exercises 95—96, find the average rate of change on the given interval. Give theexact value and an approximation to 4 decimal places. Verify that your results arereasonable by comparing the results to the slopes of the lines given in the graph. 95.
f
(
x
)
=
sin
x
For the function f1x2 = x2
, compute the average rate of change:
(a) From 1 to 2(b) From 1 to 1.5(c) From 1 to 1.1(d) From 1 to 1.01(e) From 1 to 1.001(f) Use a graphing utility to graph each of the secant linesalong with f.(g) What do you think is happening to the secant lines?(h) What is happening to the slopes of the secant lines?Is there some number that they are getting closer to?What is that number?
For what value of b is the graph of the derivative of f(x) = b^x neither a vertical stretch nor a compression of f(x)? Explain.
For the function (x^3) - x + 2:
a) what is the average rate of change over the interval [1,4]?
b) what is the instananeous rate of change at x=2?
c) what is the equation of the tangent line at x=2?
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