Question

for what values of x is
f(x) = 2x^3 -x^2 +2x
concave up?

Answer 1

you need to find \(\large\color{black}{f''(x) }\)

Answer 2

can you tell me what the first derivative will be?

Answer 3

(apply the power rule to first 2 terms, and the last term should not be a problem)

Answer 4

@ilovereyvis_x3 , excuse me, are you there?

Answer 5

sorry

Answer 6

I was drinking water

Answer 7

let me find the first derrivative

Answer 8

go ahead.

Answer 9

f'(x) = 6x^2 - 2x +2

Answer 10

yes.

Answer 11

now, the second derivative

Answer 12

f''(x) = 12x - 2

Answer 13

yes, right again

Answer 14

When \(\large\color{black}{f''(x)>0 }\), the \(\large\color{black}{f(x) }\) is concave up.

Answer 15

ok

Answer 16

Set: \(\large\color{blue}{0>12x - 2 }\) and give me the answer in interval notation that satisfies this blue statement

Answer 17

1/6 > x ???

Answer 18

yes, for any values of x that are greater than 1/6.

Answer 19

So, it is concave up over the interval of \(\large\color{black}{\left(\begin{matrix} \frac{\LARGE 1}{\LARGE 6}, +\infty\\ \end{matrix}\right) }\)

Answer 20

is that right ?

Answer 21

you are done.

Answer 22

yes, correct....

Answer 23

thank you so much

Answer 24

Not a problem!