## anonymous 5 years ago Let f(x)=7x^2-4x+6. Then the quotient (f(5+h)-f(5))/h can be simplified to ah+b for a=? and b=?

1. amistre64

are we looking for the equation of the tangent line at f(5)?

2. anonymous

I'm not sure, those are the only instructions I was given and I was never shown any sample problems, but I think that would make sense

3. amistre64

have you learned to do derivatives yet? or is that what you getting up to?

4. anonymous

ive learned

5. amistre64

good, the slope of the line is the derivative of the function at f'(5).

6. amistre64

as far as I know, "a" would equal f'(5)

7. anonymous

I dont think he is working on a derivative otherwise he would be taking the limit as h approaches 0

8. amistre64

b might = f(5) - f'(5)(h)... nadeems got a valid point :)

9. anonymous

i understand how to find the derivative, i'm just confused what the ah+b is representing in all of this

10. anonymous

f(5 + h) - f(5) = 7(5 + h)^2 - 4(5 + h) + 6 - 7(25) + 4(5) - 6 = 7(25 + 10h + h^2) - 20 - 4h - 155 = 175 + 70h +7h^2 -175 -4h 7h^2 + 66h [f(5 + h) - f(5)] = (7h^2 + 66h)/h = 7h +66

11. amistre64

might be a dummy form of the line equation... maybe h needs to be kept in as the variable?

12. anonymous

$f(x)=7x^2-4x+6$ $f(5+h)=7(5+h)^2-4(5+h)+6$ $f(5)=7(5^2)-4(5)+6$

13. anonymous

now plug in these values in to the function: $\frac{f(5+h)-f(5)}{h}\rightarrow \frac{7(h^2+10h+25)-20-4h+6-159}{h}$

14. anonymous

i see now

15. anonymous

now simplify: $\frac{7h^2+66h}{h}\rightarrow \frac{7h^2}{h}+\frac{66h}{h}\rightarrow 7h+66$

16. anonymous

so a=7 and b=66

17. anonymous

great, thanks!

18. anonymous

no problem