Question

If Q(x)=X^2-5x+1, find (Q(1+h)-Q(1))/(h).

Help me....

Answer 1

difference quotient, lets take it one step at a time

Answer 2

\[Q(x)=x^2-5x+1\]
\[Q(x+h)=(x+h)^2-5(x+h)+1=x^2+2xh+h^2-5x-5x+1\]

Answer 3

and then what's next? :| Thank You

Answer 4

so
\[Q(x+h)-Q(x)=x^2+2xh+x+h^2-5x-5h+1-(x^2-5x+1)\]
\[=x^2+2xh+h^2-5x-5h+1-x^2+5x-1\]
\[=\cancel{x^2}+2xh+h^2+\cancel{5x}+5h+\cancel{1}=2xh+h^2+5h\]

Answer 5

you see that every term without an \(h\) in it is gone, now we can divide by \(h\)

Answer 6

\[\frac{Q(x+h)-Q(x)}{h}=\frac{2xh+h^2+5h}{h}=\frac{h(2x+5+h)}{h}=2x+5+h\]

Answer 7

oh damn damn damn it was
\[\frac{Q(1+h)-Q(1)}{h}\] which is actually easier, replace all the \(x\)'s by 1
i can write it again if you like, or you can try it yourself, with \(1\) instead of \(x\)
you will get \(2+5+h=7+h\)

Answer 8

or impress you teacher, do it with \(x\) and then say "now we can replace \(x\) by any number we like to get the answer.