Someome help please

Part a.

I'm guessing this is calculus.  I know how to do it without calculus, but that's a bit more obscure.

y = 2x³ - ax² + bx + 2

We know (4,-46) is on the curve so y(4)=-46,

-46 = 2(4³) - a(4²) + b(4) + 2

0 = 128 +2 + 46 - 16a + 4b

0 = 176 - 16a + 4b

That's one equation.  Now the derivative.

y' = 6x² - 2ax + b

We know (4,-46) is stationary so y'(4)=0.

0 = 6(4²) - 2a(4) + b = 96 - 8a + b

Now we have two equations in two unknowns.  Doubling the last,

0 = 192 - 16a + 2b

Subtracting the first,

0 = (176-192) + 2b

b = 16/2 = 8

8a= 96 + b = 104

a = 104/8 = 13

Now we know

y = 2x³ - 13x² + 8x + 2

y' = 6x² - 26x + 8

y'' = 12x - 26

y''(4) = 12(4) - 26 = 48 - 26 = 22

It's positive, Concave Up Positive, it's a CUP, so a

MINIMUM

Part b.

y' = 6x² - 26x + 8

We already know one factor of y' is x-4 because y'(4)=0 so this is easy to factor:

y' = 0 = (x-4)(6x - 2)

6x=2

x = 1/3

y(1/3) = 2(1/3)³ - 13(1/3)² + 8(1/3) + 2 = 89/27

y''(1/3) = 12(1/3) - 26 = -22

Negative, concave down, a max.

(1/3, 89/27) is a MAXIMUM

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

sine

step-by-step explanation: