Question

f(x)=-2x^4-3x^3+4x^2+5x+2 find all points (x,f(x)) where there is a local minimum

Answer 1

I'm not sure how to do this, any resources would also be appreciated.

Answer 2

first find the derivative of f(x)
for critical points this = zero
then solve this equation for x for these points
a minimum has a negative second derivative

Answer 3

correction thats a positive second derivative for minimum

Answer 4

Thank you.

Answer 5

f'(x) = -8x^3 - 9x^2 + 8x + 5 = 0

Answer 6

yw

Answer 7

solving that last equation manually isn't easy - best to use wolfram alpha or a graphic calculator

Answer 8

right, looked at wolphram & the goog .. https://www.google.com/search?hl=en&tbo=d&biw=1106&bih=764&noj=1&sclient=psy-ab&q=f%28x%29%3D-2x^4-3x^3%2B4x^2%2B5x%2B2&oq=f%28x%29%3D-2x^4-3x^3%2B4x^2%2B5x%2B2&gs_l=serp.3..35i39l2.2950274.2950550.0.2951061.2.2.0.0.0.0.237.302.1j0j1.2.0.les%3Bcpmergenn..0.0...1.1.Dh_Zoa9yUik

Answer 9

What if the local min isn't on the 0?

Answer 10

in fact solving it would be a nightmare!!
sorry - i don't follow you - local minimum isn't on the o?

Answer 11

lmao, no kidding. Local min (-.48,.75) rounded to 1/100th

Answer 12

yea