differentiability
posted by matthew .
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 (x24)*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 has a relative minimum at x=2 and a relative maximum at x=2, C. f has a relative minima at x=2 and at x=2, D. f has a relative maxima at x=2 and at x=2, E. It cannot be determined if f has any relative extrema.

differentiability 
victoria
The answer is B. f' changes from negative to positive at x = 2 and positive to negative at x = 2.
Respond to this Question
Similar Questions

calculus ap
If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x24)g(x), which of the following is true? 
calculus
If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x24)g(x), which of the following is true? 
math
If g is a differentiable function such that g(x) < 0 for all real numbers x and if f'(x)=(x24)g(x), which of the following is true? 
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 following … 
Calculus
Let g and h be any two twicedifferentiable functions that are defined for all real numbers and that satisfy the following properties for all x: I) (g(x))^2 + (h(x))^2=1 ii) g'(x)= (h(x))^2 iii) h(x)>0 iv) g(0)=0 a)Justify that … 
math
Suppose p(x) is a twicedifferentiable function such that p(1) = 3, p'(1) = 0, and p”(1) = 2. Which of the following is true? 
Algebra 1 Please, check my answers!
1. What is ((12x^6 + x)) / ((4x^2))? A: 3x^4  1/4x 2. What is the greatest common factor of the terms of the polynomial 6x^3  18x^2 + 12x + 3? 
Math
The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a constant. … 
Calculus
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4x)x^3 for x>0. A. Find the xcoordinate of the critical point of f. Determine whether the point is a relative … 
Calculus
A differentiable function called f(x) achieves its maximum when x=0. Which of the following must then be true?