This is killing me (1 Viewer)

[Kutay]

Hey i really want to know how to do this question like i have an idea like i will explain.

"the curve y = f (x) has a turning point at ( -1 , 2 ). If f``(x) = 6x -8, find the equation of the function"

the prob i get like i know what to do like i first integrate that so i get y` = 3x^2 -8x +C
i understand now with the see i have to substiture something in so i can find it i tried subbing in -1 but that cant be right i have spent ages on this question and cant seem to figure it out its really annoying me, is there anyone out there that can help me please thankyou

 

[FinalFantasy]

"the curve y = f (x) has a turning point at ( -1 , 2 ). If f``(x) = 6x -8, find the equation of the function"
f'(x)=integrate ur f''(x)=int. (6x-8) dx=3x²-8x+c
at (-1,2), f'(x)=0, therefore 3(-1)²-8(-1)+c=0
.: c=-11
.: f'(x)=3x²-8x-11
f(x)=integrate f'(x)=x³-4x²-11x+c1
2=(-1)³-4(-1)²-11(-1)+c1
2=-1-4+11+c1
c1=2+1+4-11
therefore f(x)=x³-4x²-11x+2+1+4-11

(look down for words=P)

 

[Will_Sparky]

Okay, So we know that f''(x)=6x-8, so we integrate that and get that,

f'(x) = 3x² - 8x + C

We know that when x= -1, f'(x) = 0, so we sub both these values in and solve for C.

ie. 3(-1)² - 8(-1) + C = 0

therefore C= -11
therefore f'(x) = 3x² - 8x - 11

So we now integrate f'(x) to find f(x) and we get that

f(x) = x³ - 4x² - 11x + C₁

We know that when x=-1, f(x)=2 (becaue the equation passes through this point)

So we sub both values in to find C₁

2=(-1)³ - 4(-1)² - 11(-1) + C₁
2= -1 - 4 + 11 + C₁
C₁ = -4

thefore f(x) = x³ - 4x² - 11x - 4

(This is the exact same wy finalfantasy did it, but I think by using the words some people who are less mathematically minded may be able to get it better... I can't really work stuff out without them )

 

[Kutay]

Okay, So we know that f''(x)=6x-8, so we integrate that and get that,

f'(x) = 3x² - 8x + C

We know that when x= -1, f'(x) = 0, so we sub both these values in and solve for C.

ie. 3(-1)² - 8(-1) + C = 0

therefore C= -11
therefore f'(x) = 3x² - 8x - 11

So we now integrate f'(x) to find f(x) and we get that

f(x) = x³ - 4x² - 11x + C₁

We know that when x=-1, f(x)=2 (becaue the equation passes through this point)

So we sub both values in to find C₁

2=(-1)³ - 4(-1)² - 11(-1) + C₁
2= -1 - 4 + 11 + C₁
C₁ = -5

thefore f(x) = x³ - 4x² - 11x - 5

(This is the exact same wy finalfantasy did it, but I think by using the words some people who are less mathematically minded may be able to get it better... I can't really work stuff out without them )

Actually its f(x) x^3 -4x^2 -11x -4

Becareful silly mistake

 

[Will_Sparky]

Actually its f(x) x^3 -4x^2 -11x -4

Becareful silly mistake

Sorry , Calculators in another room, I did that on my hands