The function f is shown below. If g is the function defined by g(x) = | f(t)dt, write the equation of the line tangent to the graph of g at x = -6.

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: Consider the following function. 2 f(x) = x + , (-2, -3) (a) Find an equation of the tangent line to…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x= 2. X-6 f(x) = 5x - 1

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Q: Use the given graph to estimate the value of each derivative. y= f(x) 1 0. 1 (a) f'(-3) (b) f'(-2)…

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Q: The altitude h (in m) of a certain rocket as a function of the time t (in s) after launching is…

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Q: The graph of the derivative f' of a function f over the interval (0, 16) is shown. y y =f '(x) 10 12…

A: Given that: Graph of f'(x)     NOTE: As per our answering guidelines, we can only answer 1 question…

Q: Use the given graph to estimate the value of each derivative. y= f(x) 1 0, 1 (a) f'(-3) (b) f'(-2)…

A: Hence,  (a) f'(-3) = -1 (b) f'(-2) = 0 (c) f'(-1) = 0.6 (d) f'(0) = 1.5 (e) f'(1) = 3 (f) f'(2) = 0…

Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

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Q: Use the table to calculate the given derivative. h'(4) if h(x) = + f(x)g(x) 1 2 4 f(x) 0 -7 9 4 g(x)…

A: Given  h(x) = 4x3+f(x) g(x) We have to find h'(4).

Q: Using the definition of the derivative, compute f'(x) for the following functions. (a) f(r) = -3 (b)…

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Q: Find the first and second derivatives of the following function: g(t) = f'eª g'(1) = g"(t) =

A: g't = dgdt= dt3e2tdt= 3t2e2t + t32e2t = 2t3+3t2e2t = 2t+3t2e2t

Q: The derivative of the function - is equal to e Select one: a. a(2º In 2 + 1) b. e" (2ª In 2) c. e"…

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Q: If the derivative of f is given by f'(x) =e* - 3x , at which of the following values of x does f…

A: Topic- application of derivatives

Q: Find the derivative of the function g(t) =(( t-2) / (2t+1)) 9

A: we have to find the derivative of the given function g(t)=t-22t+19

Q: Let f(x) = x^2(ln x − 1) (e).Find the inflection point(s) of the graph of f, if any.

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Q: For what values of æ does the function f (x) = 12x – æ³ have a horizontal tangent line? Select all…

A: The given function is fx=12x-x3

Q: sketch the graph of the given function on the interval t ≥ 0.  2.g(t)=f(t−π)uπ(t),where f(t)=t2

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Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

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Q: For what value(s) of x does the function f(x)= 4x3-x2-2x+5 have a horizontal tangent line?  a.) x=…

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Q: The function is given by implicitly by the equation xy² +x?y+x?y² = 3. Find the derivative of y in x…

A: Here we use derivation in the function

Q: Find the domain and the derivative of the following function. c) g(x)=V1-/2-V3-x

A: Inside the root, there cannot be a negative value. Considering this we can find the domain. For…

Q: For the function f graphed below, sketch a possible graph of its derivative f'. y 3.0 2.5 2.0 1.5…

A: The derivative of a function means the magnitude of the slope of the tangent to the curve. The graph…

Q: e Find the derivative of the function g(x) = 2+ 3x g'(x) =

A: See solution below

Q: If f and g are the functions whose graphs are shown, let u(x) - f(g(x)), v(x) - 9(f(x)), and tw(x) =…

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Q: Let f(x) = 4x3 + + 2Vx – 7. Find f'(x). 15. Find an equation for the tangent line to the graph of…

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Q: Let f(x) = (x - 8)(2x +7). Find an equation for the tangent line to the graph of f = 7. at x =…

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Q: Use the given graph to estimate the value of each derivative. y A y= f(x) 1 0, 1 (a) f'(-3) (b)…

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Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: Find the equation of the line tangent to the graph of f (x) = 1+ e-*for a. x = 0 b. x = -1

A: f(x) = 1 + e-x

Q: Q2: At what points do the graphs of the functions below have horizontal tangents? 1.f(x) = x² + 4x -…

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Q: Find the derivative of the function g(t) = log2(t2 + 7)3

A: The given function is: g(t)=log2(t2+7)3 To find the derivative of this function, use the chain rule…

Q: Find the derivative of the following functions: b. f(x) &-2) %3D (4-2x- x)2

A: Suppose fx & gx are differentiable functions. The product rule of differentiation is given by:…

Q: Suppose this graph represents the 1st derivative function, f'(x). At what value(s) of x does Ax)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Shown below is the graph of f'(x), the derivative of f(x). f'(x) -3

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Q: Q2: At what points do the graphs of the functions below have horizontal tangents? 1.f(x) = x² + 4x…

A: Part 1,Given,          The function is fx=x2+4x-1 .

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

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Q: (a) Consider the following graph of a function y = f(x): -2 (i) Sketch the graph of the derivative…

A: The graph of the function f(x). We have to find the graph derivative f'(x).

Q: Let f(x)= e^x^2 . Find an equation of the line tangent to the graph of f at the point the (1,e).

A: Tangent to the graph,

Q: Given the graph of a function y = f(x) below, select the representation that best corresponds to the…

A: Given y = f(x) so dy'dx = f'(x)

Q: Let f(x) = 9 – x² The slope of the tangent line to the graph of f(x) at the point (-3,0) is The…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Using the definition of a derivative, find t'(3) given t(1) =2 -9z-1 %3D

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Q: Find the following derivative 1 g(x) = 2* · (x² + 1)

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Q: Find the first derivative f(t)-4cos (t)-10tan(t) -1

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Q: # 1) Use the given graph to estimate the value of each derivative. Then sketch the graph of f'. www…

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Q: f(x) = In(x² + 1)

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Q: 5. Let f(x) = 5x4 - -2+8√√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: C Suppose that the second derivative of a function f(x) is given by f"(x) = (x – 4)(x – 7)² In() %3D…

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Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: Find the first and second derivatives of the function. g(t) = (3t2 - 3)2 (8r?) %3D

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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: