Question

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=?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

ive learned

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

b might = f(5) - f'(5)(h)...

nadeems got a valid point :)

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

\[f(x)=7x^2-4x+6\]
\[f(5+h)=7(5+h)^2-4(5+h)+6\]
\[f(5)=7(5^2)-4(5)+6\]

Answer 13

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

Answer 14

i see now

Answer 15

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

Answer 16

so a=7 and b=66

Answer 17

great, thanks!

Answer 18

no problem