Question

suppose f(x)=3x^4-2x^2+3x. Then f''(x) =

Answer 1

can find f'(x) first?

Answer 2

(use the power rule)

Answer 3

??????????????????????????????

Answer 4

@freckles

Answer 5

apply the power rule to each of the terms,

1) what is the derivative of \(\large\color{black}{ 3x^4}\) ?
2) what is the derivative of \(\large\color{black}{ 2x^2}\) ?
3) what is the derivative of \(\large\color{black}{ 3x}\) ?

Answer 6

after you find the f '(x), differentiate f'(x) (also by applying the power rule to each of the terms) and there will be your f''(x).

Answer 7

The last thing you need is,
POWER RULE: \(\LARGE\color{black}{ \frac{d}{dx}~x^n=n~x^{n-1}}\) (where n is a constant (but not 0) , and x is the variable)

when you have a constant c times the x^n, you get,
\(\LARGE\color{black}{ \frac{d}{dx}~cx^n=cn~x^{n-1}}\)

Answer 8

ohhhhhhhhhhhhhhh so its ^^^^^^^^^^^^^?

Answer 9

I got 12x^3-4x+3x as my answer, but I think I might have done something wrong.

Answer 10

close.

Answer 11

the derivative of 3x is just 3, not 3x.

Answer 12

Oh I meant 12^3- 4x +3

Answer 13

12x^3 -4x +3

Answer 14

YES.

So, when \(\Large\color{red}{ f(x)=3x^4-2x^2+3x}\)
then \(\Large\color{red}{ f~'(x)=12x^3-4x+3}\)

Answer 15

So after you have,
\(\Large\color{red}{ f~'(x)=12x^3-4x+3}\)

find f ''(x) by (again) applying the power rule to each term (one by one)....

Answer 16

yes solomon

Answer 17

1) the derivative of \(\Large\color{blue}{ 12x^3}\) is ?
2) the derivative of \(\Large\color{blue}{ -4x}\) is ?
3) the derivative of \(\Large\color{blue}{ 3}\) is ?

Answer 18

3