# Calculus

Find the values of x that give relative extrema for the function f(x)=3x^5-5x^3
A. Relative maximum: x= 1; Relative minimum: x=sqrt(5/3)
B. Relative maximum: x=-1; Relative minimum: x=1
C. Relative maxima: x=+or- 1; Relative minimum: x=0
D. Relative maximum: x=0; Relative maxima: x=+or- 1
E. none of these

Solve without a graph

1. 👍
2. 👎
3. 👁
1. f ' (x) = 15x^4 - 15x^2
= 0 for a max/min
15x^2(x^2 - 1) = 0
x=0 or x=±1

to determine if these yield a max or a min look at the 2nd derivative
f '' (x) = 60x^3 - 30x
f "(0) = 0 , so x = 0 yields a point of inflection
f "(1) = 60-30 > 0 , so x = 1 yields a minimum
f "(-1) = -60 -(-30) < 0 , so x = -1 yields a maximum

I think B fits my conclusions

confirmation:
http://www.wolframalpha.com/input/?i=plot+y+%3D3x%5E5-5x%5E3

1. 👍
2. 👎

## Similar Questions

1. ### Calculus AB

Find a, b, c, and d such that the cubic function ax^3 + bx^2 + cx + d satisfies the given conditions Relative maximum: (2,4) Relative minimum: (4,2) Inflection point: (3,3) So this is what I have so far: f'(x) = 3a^2 + 2bx + c

2. ### differentiability

If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f prime of x equals (x2-4)*g(x), which of the following is true? A. f has a relative maximum at x=-2 and a relative minimum at x=2, B. f

3. ### Calculus

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. (If an answer does not exist, enter DNE.) f(t) = 7 t + 3/t relative maximum (x, y) = relative minimum (x, y) =

4. ### calc

let f be function given by f(x)= Ln(x)/x for all x> 0. the dervative of f is given by f'(x)= (1 - Ln(x))/x squared. a) write equation for the line tangent to the graph of f at x=e squared b) Find the x-coordinate of the critical

1. ### Calculus

Consider the function g(x) = sinxcosx. a. Find an equation of the tangent line to the graph of g at (pi/3, sqrt3/4). b. Find the critical number(s) of g on the interval [0, 2pi]. Does the function have a relative minimum, relative

2. ### Calculus

Consider the function f(x)=x^3+ax^2+bx+c that has a relative minimum at x=3 and an inflection point at x=2. a). Determine the constants a and b to make the above information true for this function. b). Find a relative maximum

3. ### Calc

Various values for the derivative, f'(x), of a differentiable function f are shown below. x=1, f'(x) = 8 x=2, f'(x) = 4 x=3, f'(x) = 0 x=4, f'(x) = -4 x=5, f'(x) = -8 x=6, f'(x) = -12 If f'(x) always decreases, then which of the

4. ### Algebra 2

Please help super confused!!! Which points are the best approximation of the relative maximum and minimum of the function? f(x)=x^3+3x^2-9x-8 a. Relative max is at (3,-13), relative min is at (-3,-19). b. Relative max is at

1. ### Calculus

Consider the function on the interval (0, 2π). f(x) = x + 2 sin x relative maximum (x, y) = relative minimum (x, y) = From when I worked out using the first derivative test, I ended up with (2π, 0) for the max and (0,0) for the

2. ### Mathematics

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. (Round your answers to two decimal places. If an answer does not exist, enter DNE.) f(x) = 3x2 − 2x

3. ### Calc

Let f be the function given by f(x)=2ln(x^2+3)-x with domain -3 is less than or equal to x which is less than or equal to 5 a) Find the x-coordinate of each relative maximum point and each relative minimum point of f. Justify your

4. ### Math

Find x-value of all points where function has relative extrema and find the Values of these extrema. f(x)= (x^2)/(ln(x))