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CALCULUS CURVE SKETCHING help need please :)?
1-Find the interval(s) where the following functions is increasing and interval(s) where the functions is decreasing
a)f(x)=2x^2 +x+1,
b) f(x) = x /(x+1)2
c) f(x) = x^2e^(−x)
2-Determine where the function is concave upward and where it is concave downward:
(a) f(x) = 3x^4 −6x^2 +x−8.
(b) f(x) = e^(x2−9).
1 Answer
- 7 years ago
f(x)=2x^2+x+1
f '(x)=4x+1
critical points = 1/4
then find a point before and after your critical which ill use 0 and 1 and insert it into f(x) and see if its positive or negative. f(0)=+++, f(1)=+++. So this one is always increasing (-inf, inf)
So for part 1 take the first derivative and set it to 0 then plug those points into f(x) to see if positive (increasing) or negative (decreasing)
f(x)=3x^4-6x^2+x-8
f '(x)=12x^3-12x+1
f ''(x)=36x^2-12
set the second derivative to 0 for inflection points.
inflection points = -1/sqrt(3) and 1/sqrt(3)
Again take points before and after, so ill use -1, 0, 1
f"(-1)=+++ f"(0)= --- f"(1)=+++
+ to - is concave down and - to + is concave up
