Find the points on the curve y=2x^3+3x^2-12x+1 where the tangent is horizontal

( - 2 , 21 ) and (1 , -6 )

The tangent is horizontal when dy / dx = 0

dy / dx = 6x² +6x - 12

equate to zero to obtain x - coordinates

6x² + 6x - 12 = 0 ⇒ 6 ( x² + x - 2 ) = 0

6( x + 2 )( x - 1 ) = 0 ⇒ x = - 2 or x = 1

substitute these values into y to obtain corresponding y - coordinates

x = - 2 → y =2(-2)³ + 3(-2)² - 12(-2) + 1 = 21 ⇒ (- 2 , 21)

x = 1 → y = 2 + 3 - 12 + 1 = - 6 ⇒ (1 , - 6 )

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

unless if u could do my questions, if not i wouldn't want to