If f(x)=x4-14x3+72x2+5x-8, find the largest interval on which f(x) is concave downward. If we write the interval as (a,b), then a= ? and b=?

Question

anonymous · Answer

take derivative twice and find where the equation is negative between two zeros

anonymous · Answer

Okay, I got the 2nd der. to be [12x ^{2}-86x=-144\]...what do i do next?

amistre64 · Answer

set it to zero

amistre64 · Answer

i always have to recall, i knw x^2 is cave up, and its 2nd derivative is positive; so if 2nd derivative is positive you got a cave up, negative is a cave down

amistre64 · Answer

where 2nd D is 0 you got inflections

amistre64 · Answer

most likely got inflections but could have some false readings that need to be dbl chkd

anonymous · Answer

I'm not sure that I'm following what you're saying...

myininaya · Answer

$$f'(x)=4x^3-42x^2+154x+5$$
$$f''(x)=12x^2-84x+154$$
set f''=0
$$12x^2-84x+154=0$$
$$6x^2-42x+77-0$$
$$x=\frac{-(-42)-\sqrt{(-42)^2-4(6)(77)}}{2(6)}$$

anonymous · Answer

your second derivative is a quadratic function that faces up. as such it will be negative between the zeros and positive outside them

anonymous · Answer

so your original function will first be concave up ( a stupid term, because it sounds just like "concave down", so what is the word "concave" doing there)  then concave down (frowning, leaning right, spilling water) then concave up again.

anonymous · Answer

got it! thanks!