ibrahimmarwa577 ibrahimmarwa577
  • 12-12-2021
  • Mathematics
contestada

Help please
Simplify the difference quotient (f(x + h) − f(x) )/h if h ≠ 0.
f(x) = x2 + 38

Respuesta :

jimrgrant1 jimrgrant1
  • 12-12-2021

Answer:

2x + h

Step-by-step explanation:

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

= [tex]\frac{(x+h)^2+38-(x^2+38)}{h}[/tex]

= [tex]\frac{x^2+2hx+h^2+38-x^2-38}{h}[/tex]

= [tex]\frac{2hx+h^2}{h}[/tex]

= [tex]\frac{h(2x+h)}{h}[/tex] ← cancel h on numerator/ denominator

= 2x + h

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