Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 months ago

Help with math question? I really cannot understand.?

I tried like 10 times and I don't seem to get this.

For the function f(x)=8x^2+2x

a) express the slope pf the secant line in terms of x and h

b) Find msec for h=0.5,0.1, and 0.01 at x=1. What value does msec approach as h approaches 0?

c) Find the equation for the secant line at x=1 with h=0.01

I know it is a lot but this is due tomorrow and this is the only problem I have left. I really cannot understand so much help can be appreciated.

1 Answer

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  • 3 months ago
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    .

    f( x ) = 8x² + 2x

    ( a )

    f( x ) = 8x² + 2x

    f( x + h )

    = 8( x + h )² + 2( x + h )

    = 8x² + 16xh + 8h² + 2x + 2h

    = 8x² + 2x + 16xh + 8h² + 2h

    slope

    = [ f( x + h ) - f( x ) ] / h

    = [ ( 8x² + 2x + 16xh + 8h² + 2h ) - ( 8x² + 2x ) ] / h

    = ( 16xh + 8h² + 2h ) / h

    = 16x + 8h + 2

    ━━━━━━━

    ( b )

    I assume msec is slope of secant line

    @ x = 1,

    𝒇o𝑟 𝒽 = 0.5; ━━━━➤ slope = 16*1 + 8*0.5 + 2 = 22

    𝒇o𝑟 𝒽 = 0.1; ━━━━➤ slope = 16*1 + 8*0.1 + 2 = 18.8

    𝒇o𝑟 𝒽 = 0.01; ━━━➤ slope = 16*1 + 8*0.01 + 2 = 18.08

    lim 𝒽 → 0, slope = 16*1 + 8*0 + 2 = 18

    ━━━━━━━━━━━━━━━━━━

    ( c )

    let f( x ) = y

    y - b = m( x - a ) where ( a, b ) = ( 1 + h, f( 1 + h ) )

    a = 1 + 0.01 = 1.01

    f( a ) = 8( 1.01 )² + 2( 1.01 ) = 10.1808

    y - b = m( x - a )

    y - 10.1808 = 18.08( x - 1.01 )

    y = 18.08x - 8.08

    ━━━━━━━━

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