Question

y=3x^3+2x^2+x+5; evaluate y' when x=3

Answer 1

can you find the derivative of the function, first?

Answer 2

lets start from a couple questions here:

what is the derivative of:
1) \(\large\color{slate}{ 3x^3 }\)
2) \(\large\color{slate}{ 2x^2 }\)
3) \(\large\color{slate}{ x }\)
4) \(\large\color{slate}{ 5 }\)

Answer 3

can you answer (any of the) above questions/

Answer 4

yeah so itd be 9x^2+4x+x?

Answer 5

Oh wait the derivative of x would just be 1 right?

Answer 6

yes

Answer 7

and derivative of 5 is zero, you know that, correct?

Answer 8

Yeah

Answer 9

Do you mind if I give it a notation, of \(\large\color{slate}{ f'(x) }\) ?

Answer 10

So now that Ive found the derivative of the function what do I do next?

Answer 11

No not at all

Answer 12

\(\large\color{slate}{ f'(x)=9x^2+4x+1 }\)

Answer 13

then, when you are asked to evaluate the derivative when x=3, you are doing the \(\large\color{slate}{ f'(3) }\)

Answer 14

So I just plug 3 in for x?

Answer 15

yes (into the \(\large\color{slate}{ f'(x) }\) )

Answer 16

\(\large\color{slate}{ f'(3) }\) = ?

Answer 17

94?

Answer 18

yes

Answer 19

very good

Answer 20

questions ?

Answer 21

Nope, got it now. Thanks!

Answer 22

Yes, good:)
(remember that derivative of a function, is a function's slope)

you welcome!

Answer 23

Is it good to just practice these?

Answer 24

Yes, any material you learn from calculus and beyond, you need to practice how to do the problems, to ensure you are ready to take the exam. This also applies to other academic courses such as physics and chemistry.