The figure below shows a graph of the given function k(x) x + 1/x. k(x) (a) Sketch a slope graph of k. k'(x) k'(x)

Q: The line in the figure shown below is the tangent line to the graph of g(x) at x = 3. Find g'(3),…

A: topic - slope of tangent line slope of a line passing through (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)…

Q: Find the values of x at which the function has a possible relative maximum or minimum point. (Recall…

A: Given the function fx=1-xe2x The derivative of the function will be f'x=2e2x-2xe2x+e2x…

Q: Using the first and second derivatives, sketch a graph for y=x^4-4x^3+1.

A: The given function is, fx=x4-4x3+1. The first derivative of fx=x4-4x3+1 is, f'x=ddxx4-4x3+1=4x3-12x2…

Q: 1+cscx 7. h(x)=- 1-cscx

A: Given the functionh(x)=1+cscx1−cscx

Q: Find the area of the triangle formed by the x-axis, the tangent to the graph of f(x) = 6x – x2 at…

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = (1 −…

A: The equation of the function  f(x) = (1 − x)(x2 − 3)2

Q: Find the derivatives w.r.t x. f(x)=x³-x. Also draw the graph of f(x) and f'(x)together and discuss…

A: Given function is: f(x)=x3-x Find the derivative of function using the power rule of derivatives:…

Q: Find an equation for the tangent line to the graph of the given function at ( – 5,32). - f(x)=x² +7…

A: Given query is to find equation of the tangent line.

Q: A graph of y = f(r) is shown. In the same coordinate system, sketch a graph of the derivative…

A: To draw the graph of the derivative of the function

Q: Find the first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the dy/dx using logarithmic differentiation y=(x2(x4+5)1/2)/(ex-x^4) 2. Find the limit lim…

A: follow next step

Q: shows the graphs of the first and second derivatives of a function y = ƒ(x). Copy the picture and…

A: The graph of y=f"(x) is a linear function. So it is of degree 1.  The graph of y=f'(x) is a…

Q: g(x) = 2x^6-5x^4+3x^3-x^2+8x-9

A: Given: g(x)=2x6-5x4+3x3-x2+8x-9 To find: The nth derivative of the function.

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

A:

Q: 3 + 3x – 5 Find the local maximum by solving the derivative P'(x)=0, – 2x + -- %3D |

A: Given Find out local maximum

Q: The graph of a function f(x) is shown below. Sketch the graph of its derivative f’(x).

A: Definition: Let f(x) be a function. f(x) is said to be increasing over some interval if f'(x)>0…

Q: Find the tangent line to g(x)=16/x-4√x at x=4

A: Slope of tangent = dg(x)/dx and equation of tangent is y-y0=slope(x-x0)

Q: Graph of f(x) is provided in the image. Sketch the graph of the derivative function f'(x).

A: In this question, we have the graph for the function f(x). Here, we need to find the graph of its…

Q: 12) Select an appropriate graph of a twice-differentiable function y f(x) that passes through the…

A:

Q: Find the values of x at which the function has a possible relative maximum or minimum point. (Recall…

A: fx=1+xe−3x

Q: Find an equation for the tangent line to the graph of the given function at (5,18). f(x) = x2 – 7…

A: Given:

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

A:

Q: c) A thin wire of 5 cm length is heated with initial temperature profile f(x) = 1 – x² and its two…

A: The given problem is to solve the temperature distribution problem, we have to formulate the partial…

Q: Find the linearization of the function given below at the specified point. f(x) = 2 ln(x) at a = 1

A: Linearization is the process of calculating the Taylor polynomial of a function up to the…

Q: Using the first and second derivatives, sketch a graph for y=x^2-4x+10

A: Given equation  y=x2-4x+10 Apply power rule to find first and second derivative f'(x)=2x-4f''(x)=2…

Q: 6) find the 2nd derivative and the graph Y’= 12-x-x^2

A: y'=12-x-x^2 Differentiate with respect to x, we get y"=-2x-1 Graph using desmos,  1) Graph of -2x-1…

Q: 15) The graphs below show the first and second derivatives of a function y = f(x). Select a possible…

A: The given graph show first and second derivatives of a function y = f(x). Here we have to select a…

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: here x-intercepts are x=-3 and x=1 so the factored form of the parabola is…

Q: The graph shown represents the graph of THE DERIVATIVE ƒ' (x) of an unknown continuous function…

A: Given, Graph of the f'(x) is shown as:

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 9/2 x +…

A: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 9/2 x…

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

A: Given: fx=x+2x-22=y To find the slope of tangent line at point (6,4) ,we need to find the value of…

Q: Find an equation for the tangent line to the graph of the given function at (-3,6). f(x) = x2 - 3…

A:

Q: Please show step-by-step solutions.

A:

Q: Graph of ln x

A: Given,         The function is fx=lnx.

Q: Find an equation for the tangent line to the graph of the given function at (- 3,13). f(x) = x² + 4…

A: From the given problem:   fx=x2+4px1,y1=-3,13   The expression for the slope of the tangent to the…

Q: To Sketch the Graphs of functions using Derivatives. Problem. Consider the function f(x) = 8x - x'…

A: Given: fx=8x2-x3f'x=16x-3x2 To sketch: The graph of the function using derivatives.

Q: A graph of y= f(1) is shown. In the same coordinate system, sketch a graph of the derivative…

A: The given graph is of a parabola with the vertex (0,-1). So, its equation is:…

Q: The graphs of the derivatives of the functions F, G & H are shown below. Which of the functions have…

A:

Q: Sketch the graph of the function ? = x3-6x2+12. Using the ff. First derivatives (critical…

A:

Q: If Z = In(x² +y²), find-

A:

Q: Consider the following graph. y a Identify, from graphs I through VI, the derivative graph and the…

A: I

Q: 1. The graph of function f(x) is given. Sketch the graph of the derivative function f'(x) below the…

A: We will sketch the graph of f'(x) as following. And also the question you asked is answered down…

Q: Consider the following graph. y a b Identify, from graphs I through VI, the derivative graph and the…

A: The given graph represents a line of form y=mx+c and from the graph, it can be seen that its…

Q: 2- The graph shows the first and second derivatives of a function y = f(x). Sketch the approximate…

A: Q2 Given, the graph of the first derivate and second derivative of a function y=f(x). The graph of…

Q: Suppose g is a continuous function on the interval (-5, 4). The graph of g', the derivative of g, is…

A: Suppose g be the continuous function and g' be the derivative of the function g. Critical point: The…

Q: Find the first and second derivatives of the function. g(x) = −7x3 + 21x2 + 5x − 64

A: Given function gx=-7x3+21x2+5x-64

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

A: 1)y=f(x)=x+2 y'=1 At (6,4), y-y1=m(x-x1) y-4=1(x-6) x-y-2=0 2) y=f(x)=x-2 y'=1 At (6,4),…

Q: Find an equation of the tangent line to the graph of the following function f at the specified…

A: The given function is f(x)=4xx2-5. Find the equation of the tangent line to the graph of f(x)=4xx2-5…