For the quartic function fx)=x^4-4x^3+8x+5, determine algebraically the:

areas of sections marked A, B, C and D

write the ratio of areas A:B:C:D in the form 1:b:c:d

Question

For the quartic function fx)=x^4-4x^3+8x+5, determine algebraically the:

areas of sections marked A, B, C and D 

write the ratio of areas A:B:C:D in the form 1:b:c:d

anonymous · Answer

attachment

shiraz14 · Answer

Step 1: Definite Integral of curve equation = 0.2x^5 - x^4 +4x^2 +5x; Differential = 4x^3 - 12x^2 + 8

shiraz14 · Answer

Step 2: Gradient of line passing through Q = 4Q^3 - 12Q^2 + 8

anonymous · Answer

how do these equations help me find the area of A, B, C and D?

shiraz14 · Answer

@smourin : Good question. Do you know the equation of the horizontal line cutting the quartic curve?

anonymous · Answer

is it the equation f(x)=x^4-4x^3+8x+5?

shiraz14 · Answer

No, that's the equation of the curve. We need to know the equation of the line before we can proceed further. Is that line shown in the diagram the x-axis? If not, please provide its equation.

anonymous · Answer

the equation of the line PS on the diagram is y=5?

anonymous · Answer

is that the right?

anonymous · Answer

equation?

shiraz14 · Answer

No, are you provided this equation in the original question? Could you please take a snapshot of the question and upload it as a JPG file so we can see it & decide how to proceed further?

anonymous · Answer

sure..

shiraz14 · Answer

OK, something's evidently amiss with this question. You need to know the equation of the line PS. This is because (just by simple inspection) one can see that the ratio of the areas will change when the line is raised/lowered accordingly.

shiraz14 · Answer

@mathmale

shiraz14 · Answer

@satellite73 : Please see if you can solve this question. Thanks.