Calculus 2 (1 Viewer)

[statsguru]

can any one help me with this question, and also wat is the best way to revise for caculus?

1: Find the stationary points of the curve y=f(x), where
f(x)= x^4 + 4x^3 - 20x^2 + 3. USe The Second Derivative to determine the nature of the stationary points.

Thanks

 

[pLuvia]

f(x)= x⁴ + 4x³ - 20x² + 3
f'(x)= 4x³+12x²-40x = 0
=x³+3x²-10x = 0
(x-2) is a factor
(x-5) is a factor
x is a factor

Test these x values for nature using the second derivative

f''(x)=3x²+6x-10

Then find the y values and then you get your coordinates of turning points.

Also find f''(x) for point of inflexion

Hope that helped

 

[Riviet]

To find points of inflexion, let f ''(x) = 0, find any x values for when this occurs, and test the point either using first or second derivative test.

 

[SoulSearcher]

Best way to revise for calculus is to do lots of questions on the rules for differentiation and integration. Lots of questions.