Question

Evaliuate the differnce quotient
f(x+h)-f(x)/ h

for f(x) = X^2 + 2x - 2

currently i have done (x+h)^2 + 2(x+h)-2 - x^2-2x - 2 / h

the answer is 2x+h+2 but each time i try to work on the problem i don't get this answer...

thanks in advance

Answer 1

f(x+h)=(x+h)^2+2(x+h)-2
= x^2+2xh+h^2+2x+2h-2

now, subtract from that f(x)

f(x)=x^2+2x-2

so f(x+h)-f(x)=2xh+h^2+2h

divide by h

= 2x+h+2

QED