when fx is 3x2x3 solve FxhfxhSolutionGiven that fx 3x2 x

when f(x) is 3x^2+x+3 solve F(x+h)-f(x)/h

Solution

Given that

f(x) = 3x² + x + 3

f(x+h) = 3(x+h)² + (x + h) + 3

= 3(x² + 2xh + h²) + x + h + 3

= 3x² + 6xh + 3h² + x + h + 3

f(x+h) - f(x) = 3x² + 6xh + 3h² + x + h + 3 - ( 3x² + x + 3 )

=  3x² + 6xh + 3h² + x + h + 3 - 3x² - x - 3

= 6xh + 3h² + h

= h( 6x + 3h + 1)

Hence,

  f(x+h) - f(x) / h = h( 6x + 3h + 1) / h

= 6x + 3h + 1

Therefore,

  f(x+h) - f(x) / h =  6x + 3h + 1