For the function fx5x24x evaluate and simplify fxh fxhfxhSo

For the function f(x)=5x2+4x, evaluate and simplify. f(x+h) = f(x+h)f(x)h

Solution

f(x)=5x²+4x

f(x+h)=5(x+h)²+4(x+h)

f(x+h)=5(x²+2xh+h²)+4(x+h)

f(x+h)=5x²+10xh+5h²+4x+4h

f(x+h)f(x) =5x²+10xh+5h²+4x+4h -5x²-4x

f(x+h)f(x) =10xh+5h²+4h

[f(x+h)f(x)]/h=[10xh+5h²+4h]/h

[f(x+h)f(x)]/h=10x+5h+4