For what value(s) x does the graph of f(x) ==- x² + 3 have a horizontal tangent? For what value of the constant c is the function fcontinuous on (-00, 00)? f(x) = {cx² + 2x, if x< 2 2x + 4, if x > 2

Q: Find the slope and the equation of the tangent line to the graph of the function at the given point.…

A: Given,f(x)= -2x +5 and the point (1-,7)

Q: The derivative in question, solve f´(2) if f(x) = x^3 – 6x^2 + 9x + 3 Determine the largest and…

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Q: Find the point on the graph of f (x) = (3x + 9)/x + 9x (x > 0) at which the tangent line is…

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Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = a - 3x + 2

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Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: Graph the function and the indicated tangent line. Graph f(x) = -4x2 and the tangent line to the…

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Q: Sketch the graph of the function f(x)=-x2 +4x-1. Find the equation of the line that is tangent to…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 19 – x²;…

A: The given data is: gx=19-x2 To find the slope of the tangent line at the point 3,10.

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: The tangent to the function, f(x) = -2x² + 3 at the point (-1, 1) is the hypotenuse of right…

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Q: Find the slope and an equation of the tangent line to the graph of the function at the specified…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: The heights on the graph of f'(x) correspond to the slopes of the lines tangent to the graph of f.…

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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: Find the equation of the line that is tangent to the graph of f(x)=(3x+1)/(4x-3) at the point where…

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Q: Find the equation of the tangent line to the graph of the function f (x) = (x2 +8) (x - 3) at the…

A: Given : f(x) = (x² + 8)(x - 3) at the point      (1, -18)

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 6 + In…

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Q: Using the second derivative criterion, find the graphs of the functions a) F(x) = x*– 8x² +3

A: Given- (a)  Fx=x4-8x2+3 To Find- The graph of the above functions using second derivative.

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent. (x, y) = Need…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: Given that f(-5)=-5  and f'(-5)=-10 , find an equation for the tangent line to the graph y=f(x) of…

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Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: Find the equation of the line tangent to the graph of the given function at the point with the…

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Q: Find the slope of the tangent to the graph of the given function at the indicated point. g(x) = 9x2…

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Q: Write the equation of tangent line to the graph of y= x^2-9x/3x-x^3 at x= 3. Chex the reasonableness…

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Q: Find all the values of x where the graph of f(x) = 2x – 24x2 + 72 - 1 has a horizontal tangent line.…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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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: The Cost and Revenue functions for the production and sale of x hair dryers is C(x)=5x+2340;…

A: Given: The Cost and Revenue functions for the production and sale of x hair dryers:

Q: Let f(x) = root ( 4x + (3x -5)10 ). Find the equation of the tangent line to the graph of the…

A: To determine the equation of the tangent line.

Q: -3. For the function f(x) = -5x - 3, find the slope of the tangent line at x =

A: We can find the slope in the following steps.

Q: Find the relative extrema of the functions f(x)=-4x2-32x-62 Identify any maximim or minimum by using…

A: To find relative extremas first we need to find critical points. These are the points where first…

Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

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Q: This is what I have so far but it says I am missing something.

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Q: If f (x)= x2 - 4x, at which point on the graph f (x) is the tangent line horizontal

A: topic - slope of tangent line

Q: Use the slopes of tangents to determine whether the function f(x) = -6x²+36x is increasing,…

A: The given function f(x)=-6x2+36x at the point x=4.

Q: Let f(x) = square root ( 4x + (3x -5)10 ).Find the equation of the tangent line to the graph of the…

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Q: Determine an equation for the line tangent to the graph of the given function at the indicated point…

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Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 7x − 4x2…

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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 all the values of x where the graph of f(x) = 2x³-36x2 + 192x 9 has a horizontal tangent line.…

A: topic - derivative of a function and point of horizontal tangent line

Q: Find the equation of the tangent line to the graph of the function f(2)=√1026 +26 at the point…

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Q: Find an equation of the tangent line to the graph of f(x)=3x3+2x when x=1.

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: Topic = Derivative

Q: Find the derivative of the function f(r) = 3x² – 12x by the definition of derivatives | f(x +h) -…

A: here option C is true 6x-12

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: