Question

Let f(x) be the function 4x2 - 6x + 11. Then the quotient
f(10 + h) – f(10)
can be simplified to ah + b for:
h
a
and
b

Answer 1

$f(x) = 4 {x}^{2} - 6x + 11$

$f(10 + h) = 4 ({10 + h})^{2} - 6(10 + h) + 11$

$f(10 + h) = 4(100 + 20h + {h}^{2}) - 60 - 6h + 11$

$f(10 + h) = 400 + 80h + 4 {h}^{2} - 60 - 6h + 11$

$f(10 + h) = 4{h}^{2} + 74h + 351$

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$f(10) = 4 ({10})^{2} - 6(10) + 11$

$f(10) = 400 - 60 + 11$

$f(10) = 351$

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Thus :

$\frac{f(10 + h) - f(10)}{h} =$

$\frac{4 {h}^{2} + 74h + 351 - (351)}{h} =$

$\frac{4 {h}^{2} + 74h }{h} =$

$\frac{4 {h}^{2} }{h} + \frac{74h}{h} =$

$4h + 74$

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$ah + b$

$4h + 74$

So :

$a = 4$

$b = 74$