Evaluate: {[f(x + h) - f(x)]/h} if f(x) = 2x^2 - 3x + 4. The result is?

Question

... 4x + 2h + 3

... 6x + 3h + 4

... 4x + 2h + 4

... 6x + 3h + 3

... 4x + 2h - 3

... 6x + 3h - 4

... 8x + 4h + 2


or none of these


What did you get?

Answer 1

f ( x+h ) = 2 ( x+h)^2 - 3 ( x+h) + 4
= 2 ( x^2 +2xh + h^2 ) - 3x - 3 h + 4
= 2 x^2 + 4 xh + 2 h^2 - 3x-3 h + 4
let us say [f(x + h) - f(x)]/h = ??
so h ?? = [f(x + h) - f(x)]
h ?? = 2 x^2 + 4 xh + 2 h^2 - 3x-3 h +4 - (2x^2 - 3x + 4 )
h ?? = 2 x^2 + 4 xh + 2 h^2 - 3x-3 h +4 - 2x^2 + 3 x - 4
with adding them up
h ?? = 4 xh + 2 h^2 - 3h
by dividing bothe sides over h
?? = 4x + 2h - 3 which is number 4 #

hope it healps any Q would be happt to answer

Answer 2

f(x + h)
= 2(x + h)^2 - 3(x + h) + 4

=2*(x^2 + 2hx + h^2) - 3(x + h) + 4

=2x^2 + 4hx + 2h^2 - 3x - 3h + 4

=(2x^2) + (4hx - 3x) + (2h^2 - 3h + 4)


[f(x + h) - f(x)]
= [(2x^2) + (4hx - 3x) + (2h^2 - 3h + 4)] - [2x^2 - 3x + 4]

=[(2x^2 - 2x^2) + (4hx - 3x + 3x) + (2h^2 - 3h + 4 - 4)]
=[ 4hx + 2h^2 - 3h]


{ [f(x + h) - f(x)]/h }
= [ 4hx + 2h^2 - 3h] / h

= h[4x + 2h - 3] / h

= 4x + 2h - 3

If h goes to zero then, you get 4x - 3, which is the derivative of f(x)

Answer 3

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