. Give four ways of describing the derivative of a function f with respect to x...

. Give four ways of describing the derivative of a function f with respect to x
A) Pictorial Description:
B) Applicable Description:
C) Rigorous Mathematical Definition:
D) Basic Mathematical Concept

Expert Solution

milcah answered 2 years ago

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x +...

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x + 1)(x + 5). Determine the intervals of x for which the function of f is increasing and decreasing Explain why a positive value for f" (x) means the graph f(x) is increasing For f(x) = 2x2- − 3x2 − 12x + 21, find where f'(x) = 0, and the intervals on which the function increases and decreases Determine the values of a, b, and...

Part A. If a function f has a derivative at x not. then f is continuous...

Part A. If a function f has a derivative at x not. then f is continuous at x not. (How do you get the converse?) Part B. 1) There exist an arbitrary x for all y (x+y=0). Is false but why? 2) For all x there exists a unique y (y=x^2) Is true but why? 3) For all x there exist a unique y (y^2=x) Is true but why?

A) Find the derivative of the function f by using the rules of differentiation. f(x) =...

A) Find the derivative of the function f by using the rules of differentiation. f(x) = 380 B)Find the derivative of the function f by using the rules of differentiation. f(x) = x0.8 C) Find the derivative of the function f by using the rules of differentiation. D)Find the derivative of the function. f(u) = 10 u E)Find the derivative of the function f by using the rules of differentiation. f(x) = 9x3 - 2x2 + 1 u u

Question 1 Let f be a function for which the first derivative is f ' (x)...

Question 1 Let f be a function for which the first derivative is f ' (x) = 2x 2 - 5 / x2 for x > 0, f(1) = 7 and f(5) = 11. Show work for all question. a). Show that f satisfies the hypotheses of the Mean Value Theorem on [1, 5] b)Find the value(s) of c on (1, 5) that satisfyies the conclusion of the Mean Value Theorem. Question 2 Let f(x) = x 3 − 3x...

For the following exercises, use the definition of derivative to calculate the derivative of each function. f(x) = 5π

For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5π

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the...

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x+13 is increasing. 3.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x−12 is decreasing. 4.Find each value of the function f(x)=−x^3+12x+9 where the line tangent to the graph is horizontal. x=

1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c)...

1) Let f(x) be a continuous, everywhere differentiable function and g(x) be its derivative. If f(c) = n and g(c) = d, write the equation of the tangent line at x = c using only the variables y, x, c, n, and d. You may use point-slope or slope-intercept but do not introduce more variables. 2) Let f(x) be a continuous, everywhere differentiable function. What kind information does f'(x) provide regarding f(x)? 3) Let f(x) be a continuous, everywhere differentiable...

Use the given function, its first derivative, and its second derivative to answer the following: f(x)=(1/3)x^3...

Use the given function, its first derivative, and its second derivative to answer the following: f(x)=(1/3)x^3 - (1/2)x^2 - 6x + 5 f'(x)= x^2 - x - 6 = (x+2)(x-3) f''(x)= 2x - 1 a) What are the intervals of increase and the intervals of decrease b) Identify local min and max points c) What are the intervals where the function is concave up, concave down and identify the inflection points

What is the derivative of f(x)=2

Find f'(x)

For the following exercises, use the definition of derivative to calculate the derivative of each function. f(x) = 3x3 − x2 + 2x + 5

For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 3x3 − x2 + 2x + 5

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