Question

Find f'(a)
f(t) = 2t^3 + t

Answer 1

Use
\[
f(t) = a t^n + b t\\
f'(t) = n a t^{n-1} +b
\]

Answer 2

In your case,
\[
f'(t) = 6 t^2 +1
\]

Answer 3

hmm, we were taught to use f(a-h) - f(a)/h

Answer 4

So u are asking to derivate the given function.... So just use the power formula..... it will be 6t^2+1

Answer 5

you sure it was not (f(a+h)-f(a))/h?

Answer 6

and if u want to use f(a-h) - f(a)/h or (f(a+h)-f(a))/h.... just put t=a+h or t=a-h...... and then t=a... and put in the formula.........

Answer 7

huge difference on f(a-h) and f(a+h)

Answer 8

(2(a+h)^3+(a+h)-(2a^3-h))/h

= (2(a+h)(a^2+2ah+h^2)-2a^3+h))/h

= 2(a^3+2a^2h+ah^2+ha^2+2ah^2+h^3)-2a^3+h)/h

= (2a^3+4a^2h+2ah^2+2ha^2+4ah^2+2h^3-2a^3+h)/h

= (6a^2h+6ah^2+2h^3+h)/h

= 6a^2 + 6ah + 2h^2 + 1

run the limit

can you do the next step?

Answer 9

@dfresenius ?

Answer 10

oh sorry was away,

Answer 11

well I ended up with 6a^2+1 after running the limit.

Answer 12

i was away working out all of those steps hadn't realized you wrote them

Answer 13

np m8, you are right

Answer 14

make sure to replace your a with a t

so we have 6t^2+1

Answer 15

You should have phrased your question by saying find the derivative using the definition as the limit of
\[
\lim_{h->0} \frac {f(x+h)-f(x)}{h}
\]