Sketch a graph of a function whose derivative is zero at exactly two points. Explain how you found the answer.

Q: Sketch the graphs of two functions that have the given derivative: f'(x)=2

A:

Q: Find the derivative of the function by definition 1 1- f(x) = 2x +3

A: Given f(x) = 12x+3 Consider f'(x) = limh→0f(x+h)-f(x)h= limh→012(x+h)+3-12x+3h=…

Q: Find the function whose derivative is 1-e2x

A:

Q: Describe geometrically when a function typically does not have a derivative at a point.

A: To describe geometrically when a function typically does not have a derivative at a point.

Q: What is the shape of a graph in application of derivatives?

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Why is the derivative of a constant function zero?

A: Consider the constant function fx=k. Apply the derivative definition as follows.

Q: Graph the derivative of the function graphed on the right.

A:

Q: Find the derivative of the function. |(7 - 0)

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Q: Find all functions ƒ whose derivative is ƒ'(x) = x + 1.

A: Given that f'(x)=x+1

Q: Explain how to graph the derivative of a function given the graph of the function.

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: The slope of the graph of the inverse tangent function is positive for all x. True or false?

A: Given: The slope of the graph of the inverse tangent function is positive for all x.

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

A:

Q: What information about a graph can be found from the second derivative?

A: What information about a graph can be found from the second derivative?

Q: Sketch the graph of the derivative for function shown.

A: Graph has a horizontal tangent between x=-2 and x=-1, at x=0 and at x=2.9, Therefore graph of f'…

Q: Determine whether each of the following statements is true or false, and explain why The derivative…

A: Given-  The derivative gives the instantaneous rate of change of a function. To determine- Whether…

Q: Sketch the graph of the derivative for function shown.

A:

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: Find a function whose square plus the square of its derivative is 1.

A: To Find a function whose square plus the square of its derivative is 1.

Q: Find the derivative of the given function

A: Given,y=cot-11x-tan-1xFormula used in thi…

Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: Match the graph of the function on the right with the graph of its derivative.

A:

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: Use the definition of the derivative to differentiate each function.

A: Given : The function is f(x ) = x3 - 6x2 - x + 30 . Definition of the derivative as a limit :  f'(x)…

Q: Find the derivative of the function, Simplity andexpress the answer positive exponents only. using

A:

Q: Sketch the graph of derivative of given functions.

A: Given graph of function is,

Q: If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Given :   If a function is decreasing with an upward concavity To find : the function's first two…

Q: The derivative of the function is equal to

A:

Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

Q: Describe how to find the slope of the tangent line to the graph of a function at a point.

A:

Q: 2. Sketch the derivative of the function whose graph is given below. Explain why you drew it the way…

A: We have to draw graph of derivatives function.

Q: What do the derivatives of a function tell you about the shape of its graph?

A: If the first derivative is positive, then the graph increases. If the first derivative is negative,…

Q: Sketch a graph of the first and second derivative for the function f(x) shown:

A: Solution is given below:

Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

Q: Sketch the graph of a function whose derivative satisfies the properties given in the following…

A:

Q: When looking at the graph of an original function, how do you know when the derivative of the…

A: To find the derivative, for your visualization, just draw the graph and the graph of its derivative.…

Q: Sketch a graph of a function whose derivative is always negative. Explain how you found the answer.

A: Sketch a graph of a function whose derivative is always negative. Explain how you found the answer.

Q: Every elementary function has an elementary derivative.

A: The elementary functions can be a constant, sum/difference of two elementary functions, product,…

Q: What is the inverse process of determining a function whose derivative is known?

A: The inverse process of determining a function whose derivative is known is called

Q: 1/3 for

A: Answer

Q: Explain how to find the derivative of the function f(x) = cxn .

A: we have to explain how to find the derivative of the given function f(x)=cxn

Q: Sketch the graph of the function f whose derivative has the given graph

A:

Q: Find the derivative of the given function.

A:

Q: Sketch the derivative of the function whose graph is below.

A: We have to sketch the derivative of the function whose graph is given .

Q: 10

A: The graph of derivative is made by observing the slope of given function

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Sketch the graph of y= x2+2/x by using the properties of the derivative.

A: Given: y=x2+2x=x2+2x⇒y'=1-2x2⇒x2-2=0 ;  ⇒x=±2 are…

Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…

Q: What do you look for when you need to match the graph of a function with the graph of its…

A: Observe the behavior of graph as the value of x increases.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: