The difference quotient D is defined by the equation Find D

The difference quotient, D, is defined by the equation

Find D if f(x)=3x^2+7x+4 and simplify answer

Solution

the given f(x)= 3x² +7x+4

given D=f(x+h)- f(x) / h

we need to submit f(x) in D

then,

D =3(x+h)² +7(x+h)+4 -(3x² +7x -6) / h

D =3(X² +h² +2xh) +7(x+h) +4-3x² -7x-4 / h

D=3x² +6xh+3h²+7x+7h+6-3x²-7x-6 / h

D= 6xh+3h² +7h/h

D =h(6x+3h+7) / h

D=(6x+3h +7)