The graph of y=​f(x) to the right gives the speed limit y along a rural highway x miles from its starting point.   ​(a) What are the maximum and minimum speed limits along this stretch of​ highway? Estimate the miles of highway with a speed limit of 50 miles per hour. ​(b) Evaluate f(16​), f(32​), and f(36​). And at what​ x-values is the graph​ discontinuous? Interpret each discontinuity.

Q: f (x) = 2л2 + 5

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Q: Determine the points at which the graph of the function has a horizontal tangent line. x2 f(x) (х,…

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Q: Use the Limit Definition of the derivative to EXACTLY evaluate the derivative. f(x) = 3/x

A: The solution of the problem is given in the next step.

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Q: Use the limit definition of the derivative to find f'(x). f(x) = 3 + 2x – x²

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Q: Graph y = - x“ + 2x² – 10 function using x- and y-intercepts, critical points, points of inflection,…

A: Plot the graph for f(x).

Q: Graph f(x) = x +2x -5 and the tangent line to the graph at the point whose x-coordinate is -2.

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Q: Find the equation of the line tangent to the graph of the function at the indicated point. 5) f(x) =…

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Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

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Q: The function f is given by f(x) = -1-e-. What is the equation of the line tangent to the graph of f…

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Q: What is the slope of the graph of f (x) = x3 - 4x2 + 6 at x = 2? Write the equation of the line…

A: Given :        The function f(x) = x3 - 4x2 + 6    To find the slope of the graph f(x) = x3 - 4x2 +…

Q: What is the slope of the line tangent to the graph of a function defined by f(x)= x² + √x at x=1?

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Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

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Q: f(x ) = x -3 х 2—9

A: Simplify the function then take derivative and draw the graph.

Q: Using the criterion of the first derivative, find the graph of the function: F(x) = 114 (x*) + 4,…

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Q: Find the points where the graph of the function has horizontal tangents. f(x) = 3x^2 + 7x - 5

A: We have to find the points where the graph of the function has horizontal tangents.…

Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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A: Given function is, f(x)=x2

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A: We will use following properties of f(x) to draw its graph  # vertical asymptotes are vertical…

Q: Use the limit definition to find the derivative of the function. f(x) = x2 – 4x +3 -

A: f(x)=x2-4x+3 TO find: The derivative using limit definition

Q: he figure shows the graph of the derivative f' of a function f. yA y= f'(x) -2/

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

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A: Given statement : If the graph of a function has three x-intercepts, then it must have at least two…

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A: To determine equation of tangent line at given point.

Q: Find the derivative of the function using the limit definition of the derivative. f(x) = 3x - 8

A: We have to find the derivative using limit definition of the derivative for the function: fx=3x-8 We…

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A: The objective is to determine the points where the graph of function has horizontal tangent line.

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Q: Determine the equation of the line tangent to the graph of f ( x ) = 3 x 2 − x + 4 at x = − 1.  Give…

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Q: Find the slope of the line tangent to the graph of the function defined by f(x) = 3x2 – 4 at (1,…

A: Solution:Given        f(x)=3x2-4   at (1,-2)To find:Slope of the line tangent to the graph The…

Q: Find the slope of the line tangent to the graph of the function defined by f(x) = x2 – 3x + 4 at…

A: It is given that, f(x)=x2-3x+4   Slope of any function or tangent of any function is defined as the…

Q: Find the function of the derivative f'(x)= -12x+5 and with the graph passing through (-2,5)

A: Given, f'(x)= -12x+5

Q: 3. Use the limit definition of the derivative to find the derivative of the function. a) f(x) = 2x²…

A: Given query is to find the derivative using definitely.

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

A: To sketch the graph

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

Q: Find an equation of the tangent line to the graph of y = f(x) when x = 2 if f(2) = -6 and f'(2)= 5.…

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Q: Use the limit definition of the derivative to find the derivative of: f(x) = x^2+5x-2

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Q: 1/3 for

A: Answer

Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1.

A: The equation of the curve is given by fx = 3x2-x-5 The point is x = 1 Formula Used: mtan = dfdxx=1…

Q: Find the indicated derivative. f'(-5) = If f(x) = x², find f'(-5). X

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 4 +9 In…

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Q: Suppose there is a function called f(x). How do you find the slope, m, of the line that is tanget to…

A: We have give,

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: True or false, for the graph of y=2^x, the slope of the tangent line is the same as the function…

A: slope of tangent line to a curve y = f(x) is given by          m = dydx

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: