Question

3. Given the following polynomial function: f(x) = 3x^4 + 2x^3 – 2 b. Find critical value(s) c. Find interval(s) where f(x) is increasing. d. Find interval(s) where f(x) is decreasing e. State any Max or min. f. Find interval(s) where f(x) is concave up g. Find interal(s) where f(x) is concave down h. State any point(s) of inflection

Answer 1

\[y = 3x ^{4}+2x ^{3}-2\]

Answer 2

For critical values take dy/dx =0

Answer 3

\[\frac{dy}{dx}=12x^3+6x^2\]

Answer 4

\[\frac{d^2y}{dx^2}=24x^2+12x\]

Answer 5

how do i find the critical value

Answer 6

after getting the derivative

Answer 7

0 sorry about the answer earlier

Answer 8

\[0=12x^3+6x^2\]

Answer 9

it says state any points of inflection have any clue?

Answer 10

do the same to the second derivative. its critical points are usually inflection points.

Answer 11

when a first derivative is positive, it's original function is increasing.
negative, decreasing
when it is zero, the original equation is flat (like at a minimum or maximum.

Answer 12

second derivative:
if it is positive, the original function is concave up
negative, concave down.
zero = inflection point

Answer 13

notice a difference between increasing and concave up. a curve can be decreasing, but doing so at a slower and slower rate, thus concave up.