Let f(x) = x2. Show that for any distinct values of a andb, the slope of the tangent
Chapter 2, Problem 27(choose chapter or problem)
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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