[tex]f(x) = 4 {x}^{2} - 6x + 11[/tex]
[tex]f(10 + h) = 4 ({10 + h})^{2} - 6(10 + h) + 11 \\ [/tex]
[tex]f(10 + h) = 4(100 + 20h + {h}^{2}) - 60 - 6h + 11 \\ [/tex]
[tex]f(10 + h) = 400 + 80h + 4 {h}^{2} - 60 - 6h + 11 \\ [/tex]
[tex]f(10 + h) = 4{h}^{2} + 74h + 351[/tex]
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[tex]f(10) = 4 ({10})^{2} - 6(10) + 11[/tex]
[tex]f(10) = 400 - 60 + 11[/tex]
[tex]f(10) = 351[/tex]
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Thus :
[tex] \frac{f(10 + h) - f(10)}{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} + 74h + 351 - (351)}{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} + 74h }{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} }{h} + \frac{74h}{h} = \\ [/tex]
[tex]4h + 74[/tex]
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[tex]ah + b[/tex]
[tex]4h + 74[/tex]
So :
[tex]a = 4[/tex]
[tex]b = 74[/tex]
