# Calculus

True or False: Consider the following statement:
A differentiable function must have a relative minimum between any two relative maxima.
Think about the First Derivative Test and decide if the statement is true or false.

I want to say that its true and that the question is just trying to make me second guess myself. If you have two relative maxima, then there has to be change between them, which (I believe) would result in a relative minima. Is this right?

1. 👍
2. 👎
3. 👁
1. it's true

1. 👍
2. 👎

## Similar Questions

1. ### 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

2. ### Algebra 2 help :)

Any number in the form of a+-bi , where a and b are real numbers and b not equal 0 is considered a pure imaginary number. TRUE OR FALSE The minimum value is the smallest y-value of a function. T RUE OR FALSE i2 = square root of

3. ### 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

4. ### Environmental Science

1. A prion is an infectious, self-reproducing protein structure. True X False 2. As one organism eats another, toxins can be spread throughout the food chain. True False x 3. The problem with DDT in the environment is that it

1. ### calculus

If a function f is continuous for all x and if f has a relative minimum at (-1,4) and a relative minimum at (-3,2), which of the following statements must be true? (a) The graph of f has a point of inflection somewhere between x =

2. ### 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

3. ### algebra 2a help

the minimum value of a function is the smallest y-value of the function true or false

f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x -8,-3,0,3,8 f'(x)-4,-2,0,4,5 If f ′(x) is always increasing, which statement about

1. ### Environmental Science

1. Decibel is a measurement of the amount of pollution (True or False) 2. Non-Point-Source pollution can be traced to one specific source (True or False) 3. Point-Source pollution is pollution that comes from identifiable

2. ### math

Let f be the function defined as: f(x) = (x^2 - 4)/ (x-2) if x≠2 1 if x=2 Which of the following statement(s) about f is true? A. f has limit at x=2 B. f is continuous at x=2 C. f is differentiable at x=2

3. ### math

Is each biconditional statement true or false? Select True or False for each statement. A polygon is a square if and only if the polygon has exactly four sides. true or false A polygon has exactly five sides if and only if the

4. ### Calculus (Urgent Help)

Okay, I need major help! Can someone tell me if these statements are true or false ASAP please. Thank you. 1. If ƒ′(x) < 0 when x < c then ƒ(x) is decreasing when x < c. True 2. The function ƒ(x) = x^3 – 3x + 2 is