Question

Whats the f' and f'' of : f(x)= (x^2)/9 + (x-4)^(2/3)?

Answer 1

Was it given to you?

Answer 2

No, this is why I ask the question haha

Answer 3

Ok

Answer 4

Do you have an idea of how to solve functions?

Answer 5

Yeah but I have some difficulties with that one! Can you help me or not?

Answer 6

\[\Large f(x) = \frac{ 1 }{ 9 }x^2 + (x-4)^{2/3}\] yes?

Answer 7

yes !

Answer 8

Do you know how to find the derivative of the 1/9 x^2? Use the power rule: multiply by the exponent, reduce the exponent by one.

Answer 9

this is the correct answer

Answer 10

\[\frac{ 2((x-4)^{4/3}-1) }{ 9(x-4)^{4/3} }\]

Answer 11

this is the answer but I can't arrive to this answer by myself and I don't know why so that's why I need to know the complete calcul :(

Answer 12

Don't worry about the answer yet. Do it step by step.

Answer 13

I do this but it doesn't work..

Answer 14

The answer will come from algebra, first you have to do calculus... do you know how to differentiate each term?

Answer 15

no :p I need the solution

Answer 16

The function, the first derivative and the second derivative from left to right.\[\left\{\frac{x^2}{9}+(x-4)^{2/3},\frac{2 x}{9}+\frac{2}{3 \sqrt[3]{x-4}},\frac{2}{9}-\frac{2}{9 (x-4)^{4/3}}\right\} \]

Answer 17

\[\Large f(x) = \frac{ 1 }{ 9 }x^2 + (x-4)^{2/3}\]
\[\Large f'(x) = 2*\frac{ 1 }{ 9 }x^{2-1}+ \frac{ 2 }{ 3 }(x-4)^{2/3 -1}\]

Answer 18

Do you know the rules of finding a derivative?

Answer 19

yes I know the rules but I cant do this number

Answer 20

and thanks for the people that try to help me :)

Answer 21

see it, i forgot the last step but now i have done it

Answer 22

Okay, its hard to read it but thanks anyway haha :)