Question

Given that the tangent line to the graph of y=f(x) at the point (2,5) has the equation of y=3x-1, find f '(2).

Answer 1

I think it's going to be 3 because the derivative of y=3x-1 is y'=3, and that would be the answer regardless of whatever value you substitute (in this case you can't because there's no variable).

Answer 2

how did u get 3?

Answer 3

For the derivative, we know that y=3x will become 3, because \[3x ^{1} \] 's derivative is going to be \[1 \times 3^{1-1}\] . Refer to the power rule general formula. Does it make sense?

Answer 4

maybe im dumb, but that doesnt make sense whatsoever.

Answer 5

i get the bits and pieces that your trying to say, but when i group the bits and pieces together, i dont understand the general thing your trying to express.

Answer 6

Oh. Well do you know what the power of a function rule is (aka the power rule)?

Answer 7

no.

Answer 8

we are just starting derivatives.

Answer 9

oh no wonder. still that's a bit weird cos you have to know the power rule in order to solve it. But the power rule is:

if f(x) = x^n, where n is a real number, then f'(x) = nx^n-1.

Answer 10

the only formula we have is \[f'(x _{o})=\lim_{x \rightarrow x _{o}}\frac{ f(x)-f(x _{o}) }{ x-x _{o} }\]

Answer 11

ugh. i hated that formula, first principles was never my favorite. but for this you'll have to substitute f(x) as 3x-1, and t(xa) as 2. please tell me you've learnt limits.

Answer 12

\[=\lim_{x \rightarrow 2}\frac{ (3x-1)-2 }{ x-2 }\]
\[=\frac{ 3 }{ 0 }\]

=i am stuck cuz its not 3.

Answer 13

does that make sense?

Answer 14

yeah, thanks