Question 296583: find the largest open interval at which function is concave up or concave down and find the location of any points of inflection.
f(x)= x^4+8x^3-30x^2+24x-3
Please help with steps
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the largest open interval at which function is concave up or concave down and find the location of any points of inflection.
f(x)= x^4+8x^3-30x^2+24x-3
------------------------
f'(x) = 4x^3
+ 24x^2 - 60x + 24
Solve f'(x) = 0
x = -7.975.. or x = 0.5154 or x = 1.4598
---
f"(x) = 12x^2 + 48x - 60
Find f"(-7.975) > 0 so f(x) is concave up in that region
Find f"(0.5154) < 0 so f(x) is concave down in that region
Find f"(1.4598) > 0 so f(x) is concave up in that region
--------------------------
Solve f"(x)= 0
x = x = -0.5 or x = 1
This locates points of inflection.
------------------------
Concave up: (-inf,-0.5)U(1,+inf)
Concave down: (-0.5,1)
------------------------------
Cheers,
Stan H.
|
|
|
