f(x)=x^4-14x^3+72x^2+9x-10

find the largest interval on which f(x) is concave downward. If we write the interval as (a,b), find a and b

Question

f(x)=x^4-14x^3+72x^2+9x-10

find the largest interval on which f(x) is concave downward. If we write the interval as (a,b), find a and b

amistre64 · Answer

in other words, find the 2 inflection points

amistre64 · Answer

set f'' to 0 and that should do it for this ....

anonymous · Answer

okay can you just tell me how to do it. i dont understand you

amistre64 · Answer

if the site doesnt die on me i might be able to scrounge up someting :)

amistre64 · Answer

$$\frac{d^2}{dx^2}x^n\to n(n-1)x^{(n-2)}$$
is all you are doing to this

amistre64 · Answer

$$f(x)=x^4-14x^3+72x^2+9x-10$$
$$f''(x)=4.3x^2-14.3.2x+72.2.1x0+9.1.0 -10.0.-1$$
$$f''(x)=12x^2-84x+142$$

set that to zero and they should define your interval of concavity

amistre64 · Answer

might be able to factor out a few things to get the numbers down too

amistre64 · Answer

6,24,72

3,12,35

f'(x) = 3x^2 -12x +35