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Lina20 [59]
3 years ago
15

1. For the function f(x) = x2, Find the slope of the secant line joining (1,f(1)) and

Mathematics
1 answer:
goblinko [34]3 years ago
3 0

The slope of the line connecting two points (<em>a</em>, <em>b</em>) and (<em>c</em>, <em>d</em>) is

(<em>d</em> - <em>b</em>) / (<em>c</em> - <em>a</em>)

i.e. the change in the <em>y</em>-coordinate divided by the change in the <em>x</em>-coordinate. For a function <em>y</em> = <em>f(x)</em>, this slope is the slope of the secant line connecting the two points (<em>a</em>, <em>f(a)</em> ) and (<em>c</em>, <em>f(c)</em> ), and has a value of

(<em>f(c)</em> - <em>f(a)</em> ) / (<em>c</em> - <em>a</em>)

Here, we have

<em>f(x)</em> = <em>x</em> ²

so that

<em>f</em> (1) = 1² = 1

<em>f</em> (1.01) = 1.01² = 1.0201

Then the slope of the secant line is

(1.0201 - 1) / (1.01 - 1) = 0.0201 / 0.01 = 2.01

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