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P( - , )

Step-by-step explanation:

The derivative of y is the gradient of the slope.

Given

y = 2x³ + 3x² + 2, then

= 6x² + 6x , equate to -

6x² + 6x = - ( add -

6x² + 6x + = 0 ( multiply through by 2 )

12x² + 12x + 3 = 0  ( divide through by 3 )

4x² + 4x + 1 = 0 ← in standard form

(2x + 1)² = 0 ← in factored form

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -

Substitute this value into y for corresponding y- coordinate

y = 2(- )³ + 3(-

  = 2(- ) + 3( ) + 2

  = - + + 2 =

Thus P = ( - , )

step-by-step explanation:

answer: d. $20

step-by-step explanation:

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