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Question

In the above figure, slope of the secant will give the rate of change of f(x) at x = (a+b)2


A

True

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B

False

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Solution

The correct option is B

False


Let’s find the slope of the secant to decide if the given statement is correct. The two end points of the given secant are (a, f(a) ) and (b, f(b)).

The slope of this line is f(b)f(a)ba is

If you remember how we defined average rate of change, you can easily find that the slope is nothing but the average rate of change of f(x) with respect to x over the interval [a,b].

The rate of change at x=(a+b)2

limh0=f((a+b)2+h)f((a+b)2)h

This is not equal to average rate of change for any ‘a’ and ‘b’, even though it could give the average rate of change for some f(x), a and b

So, the given statement is false


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