For f with derivative as in Figure 13: Is f(c) a local minimum or maximum? Is f a decreasing function? FIGURE 13 Graph of derivative f'.

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

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Q: Find an equation of the tangent line to the graph of f (x) = 1/√x at x = 9.

A: The equation of the graph is given as, fx=1x We need to find the equation of the tangent to the…

Q: Determine the point(s) at which the graph of the function has a horizontal tangent line. f(x) =…

A: Now slope of the tangent line is the derivative of the given function. So differentiating f(x) with…

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Given, f(x)=e3x, 0,1 We need to find an equation of the tangent line to the graph of the function at…

Q: The following figure gives the graph of the derivative of a continuousfunction ƒ that passes through…

A: The graph limit of the derivative of a continuous function is -3≤x≤1. The limit of variable x at y=0…

Q: Define the derivative of f(x) at x =a

A: For a function f(x), the derivative is defined as: Now at x=a, the derivative is defined as:

Q: Find an equation for the tangent line of the graph of f(x)=x^2-1 at (4,15).

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Q: Consider the function y = x² In(x³). At which point the tangent line to the graph of this function…

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Q: Find an equation of the tangent line to the graph of f(x)

A: Given function ,         fx=3-Yxx+5at -1,1To find the slope , we differenntiate the function fx…

Q: Find an equation of the tangent line to the graph of f(x) f(x) = 1/√5x at x = 9.

A: Given equation of curve

Q: Here is the graph of the second derivative of a function g(x). g"(x) Where does g(x) have a point of…

A: Inflection point is at that x value where the double derivative of the function is 0.

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Let f(x) = √|x-1| Find the equation of the tangent line to the graph of f at the point where x = -1

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

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Q: Define the derivative f'(a) of a function f at x =a.

A: To define: The derivative f'(a) of a function f(x) at x=a

Q: Find an equation for the tangent line to the graph of f(x) at x = 1.

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Q: V-メ (3 23

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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…

Q: find the equation of the tangent line to the graph of f(x)=x^2(x^1/2 +1) at x=4

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

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Q: Find an equation of the tangent line to the graph of fat the given point. f(x) X -

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Q: Match the graph of the above function with the graph of its derivative. 0 ㅇ O 수 +

A: The given graph of the function is the graph of a semi circle. Or positive side of the circle.

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = el-x,…

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Q: Find the equation of the tangent line to the graph of the function f(x) = x² +x – 1 at the point…

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Q: Describe the slope of the tangent line to the graph of f(x) = e* for the following. (a) x-- (b) x-0

A: The slope of a line is the tangent of the angle that the line makes with the x-axis. The slope of…

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: Find an equation of the tangent line to the graph of f at the given point. (5-) X + 3 f(x) X -1 2

A: Find an equation of the tangent line to the graph of f at the given point. First differentiate the…

Q: Find an equation for the tangent line to the graph of f at the given point: f(x)=\sqrt(x-1) x=(5,2)

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Q: Use the fact that the derivative of the function g(x)=√x is g"(x)=1/2√x to find the equation of the…

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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: 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: Find the tangent line to the graph of f(x)=(x+1)/(x-1) at the point (2,3)

A: As we know that; The slope of the tangent line to the curve at a given point is equal to the first…

Q: The slope of the tangent line to the graph of f(x) = at a = 1 is: ¤ + x

A: Given:f(x) = xx + x

Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: Find the point on the graph of h(x) with the largest slope, that is, the (a) point where the tangent…

A: Given function is         h(x) = -3x5-5x4+20x3+60x To find the largest slope of h(x) at the tangent…

Q: Find an equation of the tangent line to the graph of f(x) at the given point. f(x)= 2 / x^(3/4)  at…

A: Given function f(x)

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 3/2 x +…

A: Here the given function

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

A: Consider the function  f(x)=x2−1x2+x+1 Point (1,0)

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

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

A: given : g(x) = 83x +3∴ differentiate with respect to x g'(x) =83

Q: Let f(y) -8+ In Determine the derivative f'(y) : ||

A: The function is given as, fy=-1-8+lny. The derivative of the function , f'y=-0-0-8+lny2=0. The…

Q: a) What is the slope of the tangent line to the graph of f at x= n ?

A: Given, fx = 4cos2x -2esin3x  We have to to find the slope of the tangent line to the graph of f at x…

Q: Find the slope of the tangent line to the graph of f(x) at the point (1,2). The function is…

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

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

A: Graph

Q: Find an equation of the tangent line to the graph of the function f (x) = (2x – 1) In x when x = 1

A: Given function is f(x)=(2x-1)ln(x) Slope of the graph of f(x) at any point is given by, m=f'(x)