# Calculus

posted by .

What is the point of inflection of the function f(x)=x^3-8x^2+5x+50? Is the local extrema at f(1/3)=50.8 max and f(5)=0 min?

For the second derivative I got f(x)=6x-16 and then got x=16/6 when set to zero.

• Calculus -

3 x^2 -16 x + 5 = 0
first derivative
at x = {16 +/-sqrt(256-60)]/6
or [16+/-14]/6 = 5 or 0.3333

second derivative
6 x - 16
is that + or - at the two points where the slope is zero?
at x = .333
2 - 16 is negative so maximum there
at x = 5
6x - 16 = 30-16 is positive so minimum there

## Similar Questions

1. ### Calculus

R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM?
2. ### calculus

(a) find the intervals on which f is incrs or decrs. (b) find the local min/max values of f. (c) find the intervals of concavity and the inflection points. f(x)=(lnx)/sqrtx I took the derivative and got 2-lnx/2x^3/2 take the values …
3. ### calc.

I'm having a lot of trouble with this problem: Sketch the graph and show all local extrema and inflections. f(x)= (x^(1/3)) ((x^2)-175) I graphed the function on my graphing calculator and found the shape. I also found the first derivative: …
4. ### calculus

a function has a local maximum at x=-2 and x=6 and a local minimum at x=1. how do u find the concavity of this function and point of inflection?
5. ### Calculus

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection …
6. ### Calculus

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection …