If fx x2 3x 4 find and simplify fx h fxhSolutiongiven f

If f(x) = x^2 + 3x + 4, find and simplify f(x + h) - f(x)/h

Solution

given

f(x)=x²+3x+4

f(x+h)=(x+h)²+3(x+h)+4

f(x+h)=x²+2xh+h²+3x+3h+4

[f(x+h)-f(x)]_/h

=[(x²+2xh+h²+3x+3h+4)-(x²+3x+4)]_/h

=(2xh+h²+3h)_/h

=(2x+h+3)