Question

Multiple Choice?
Caculus?????

the derivative of f is given as
2(x-1)(2x+1)^2(5x-2 )

f has a relative maximum at
x = 1 only
x = 2/5 only
x = 1/7 only
x = -1/2 only
x = 1 and x = -1/2

Answer 1

Find the sign of the derivative function in the intervals: (-infinity, -1/2) ; (-1/2, 2/5), (2/5, 1) and (1, infinity)

Answer 2

how do I do that?

Answer 3

set each = to0?

Answer 4

that would be - 1/2 and 2/5

Answer 5

Pick a point in each interval and evaluate the derivative at that point.
Example, in the interval (-infinity, -1/2) pick -1 and evaluate the derivative.

Answer 6

f'(x) = 2(x-1)(2x+1)^2(5x-2 )
f'(-1) = ?
f'(0) = ?
etc.

Answer 7

okso I know I have my max when...

Answer 8

when f'(x) changes from positive to negative.

Answer 9

got it. Thank you so much!

Answer 10

You are welcome.

Answer 11

I'll finish tomorrow I am exhausted :) but I understood so I feel good about it

Answer 12

thanks again

Answer 13

Alright.

Answer 14

Actually one can can ignore the factor (2x+1)^2 since it is always positive and hence does not affect the sign of the derivative. So one has to study the sign of the derivative of
(x - 1) (5 x - 2)
-Infinity 2/5 1 +Infinity
(x-1) - - 0 +
(5 x -2) - 0 + +
Sign of product + 0 - 0 +
function incr. Max decr. Min incr

So relative maximum at 2/5 only

Answer 15

@eliassaab that's what I got! Thanks!