Let f(x) = x2. Show that for any distinct values of a andb, the slope of the tangent

Chapter 2, Problem 27

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Let \(f(x)=x^{2}\). Show that for any distinct values of \(a\) and \(b\), the slope of the tangent line to \(y=f(x)\) at \(x=\frac{1}{2}(a+b)\) is equal to the slope of the secant line through the points \(\left(a, a^{2}\right)\) and \(\left(b, b^{2}\right)\). Draw a picture to illustrate this result.

Equation Transcription:

Text Transcription:

f(x)=x^2

a

b

y=f(x)

x=1/2(a+b)

(a,a^2)

(b,b^2)

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