Brief Calculus.

Question

Find difference quotient for f (x) = 3x²-2x+4

Step by step please.

Answer 1

f'(x) = 6x-2

f'(x) = [f(x+h) - f(x)]/h

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

=[3x^2 + 6xh + 3h^2 -2x -2h +4 -3x^2 +2x -4]/h

=[6xh +3h^2 -2h]/h

= 6x +3h -2

the limit as h approaches zero = 6x+3(0)-2 = 6x -2

the purpose of finding the difference quotient is to calculate the derivative

which is what you get by taking the limit as h goes to zero

Answer 2

a) f (x+h) = 3(x+h)^(2) -2(x+h)+4 , you simply substitute (x+h) for x in the equation

b) f(x+h)-f(x) = 3(x+h)^(2) -2(x+h)+4-(3x^(2)-2x+4)=6hx+3h^(2)-2h

c) f(x+h)-f(x) / h = 6x-2+3h