How do you find the equation of the secant line of #f(x)=x^25x# through the points [1,8]?
The pointslope form of the equation of a line is:
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We have
When
#x=1 => f(x) = 15 = 4#
When#x=8 => f(x) = 6440 = 24#
So the required secant line passes through the points
We can calculate the slope of the secant line using
#m=(Delta y)/(Delta x) = (24(4)) / (81) = 28/7 = 4#
So using the factthat the line passes through
# y  (4)=4(x1) #
# :. y +4 = 4x4 #
# :. y = 4x8 #
NB: We could have equally used the other coordinate
Which we can confirm graphically:
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To find the equation of the secant line of the function ( f(x) = x^2  5x ) through the points ([1,8]), you can use the pointslope form of a linear equation.

First, find the slope of the secant line using the two given points ([1,8]) and another point on the secant line. You can choose any point on the line, but for simplicity, let's choose a second point ( [x, f(x)] ) on the line.

The slope of the secant line is given by the formula: [ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} ]

Plug the coordinates of the given points into the formula to find the slope: [ \text{Slope} = \frac{f(x)  8}{x  1} ]

Now, substitute the function ( f(x) = x^2  5x ) into the formula: [ \text{Slope} = \frac{x^2  5x  8}{x  1} ]

Next, simplify the expression: [ \text{Slope} = \frac{x^2  5x  8}{x  1} = \frac{(x  1)(x  8)}{x  1} ] [ \text{Slope} = x  8 ]

Now that you have the slope, you can use the pointslope form of the equation of a line to find the equation of the secant line: [ y  y_1 = m(x  x_1) ]

Substitute the coordinates of the given point ([1,8]) and the slope (m = x  8) into the pointslope form: [ y  8 = (x  8)(x  1) ]

Expand and simplify the expression: [ y  8 = x^2  9x + 8 ] [ y = x^2  9x + 16 ]
Therefore, the equation of the secant line of ( f(x) = x^2  5x ) through the points ([1,8]) is ( y = x^2  9x + 16 ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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