If the graphs of two di£erentiable functions ƒ(x) and g(x) start atthe same point in the plane and the functions have the same rateof change at every point, do the graphs have to be identical? Givereasons for your answer.

Q: Find the instantaneous rate of change for function at the given value. F(x) = x2 + 2 at x = 0

A: Given a function, F(x) = x2 + 2 at x = 0 To Find the instantaneous rate of change for function at…

Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

Q: If the instantaneous rate of change of f(x) at (8, −7) is 9, write the equation of the line tangent…

A: It's given that the instantaneous rate of change  of  f(x) at  (8,-7) is 9 . We have to find the…

Q: Suppose the function fis differentiable everywhere, and the graph of y - f(x) always lies above the…

A: given: the function f is differentiable everywhere and the graph of y=f(x) always lies above the x…

Q: With the given graph, estimate the instantaneous rate of change at x= -1 and show the steps. Next,…

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Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

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Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much…

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Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 2 if g(2) = −3 and g'(2) = 4.…

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Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2…

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Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

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Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: In a simple physical apparatus, the distance x cm and y cm are connected by the relation 1.1 1…

A: Distance x cm and y cm are connected by the relation 1x+1y=19 ....(1) x is increasing at the rate of…

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: A bacterial population B is known to have a rate of growth proportional to B itself. If between noon…

A: We will use the exponential growth equation of bacteria .

Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

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Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

Q: 4. Find all points on the curve y = log (x³ – x) at which the tangent line is horizontal.

A: We will find all the points on the curve at which the tangent line is horizontal using calculus as…

Q: What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the point.12

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

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Q: Find the slope-intercept equation of the line tangent to the graph of y = e when x = In 3. O y = 3x…

A: The given function is y=ex and the point x=ln3

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

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Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

Q: 9. If the volume and radius of a sphere are functions of time,what is the relationship between the…

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Q: If the slope of the tangent line to the graph of y-f(x) at x-a is m(a)=20+1, and f(1)-5, then what…

A: We have to find function

Q: A particle is moving on the x-axis and the position of the particle at time t is given by x (t),…

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Q: Find an equation of the tangent line to the graph of y=e^-x^2 at the point (2,1/e^4)

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Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

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Q: projected that, t months from now, the population of a certain town will be growing at the rate of…

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Q: Consider a scenario in which a 20ft tall lamppost lights up a street. (a) A 5ft tall woman stands…

A: Length is a measure of distance. In the International System of Quantities, length is a quantity…

Q: 2 Refer to the graph above and without making any computa- tions find: The average rate of change…

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Q: What is the slope of the tangent line that touches the graph of Iny+e2x-1 = 3y – 4x at the point A 1

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Q: Suppose that value of wine respect to time is given following function V = 100e ve. How long will it…

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

A: Given, fx=4xx2+6 Now we find the slope ddx4xx2+6 Now by using the quotient rule,…

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

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Q: Suppose that the marginal propensity to consume is dC -0.2y = 0.8 - e dy (in billions of dollars)

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Q: i. Find the equation of the tangent to the graph of g at (4, 2).

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Q: find the instantaneous rate of change of the function at the given x-value. f(x)=x2 + 3x at x=4

A: f(x)= x2+3x  and x=4

Q: If the instantaneous rate of change of f(x) at (6, −8) is 4, write the equation of the line tangent…

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Q: The slope of the tangent line to the graph of the function y = 8/T- 4 at (16, 28) is O 4 O -1.75 O…

A: Slope : It is the Differentiation of y with respect to x at a given point.

Q: To three decimal places, the slope of the tangent to the curve f (x) = log, x , at x = 2 is:

A: First we have to find the differential equation for slope of this function.

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5V9x2 –…

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Q: Consider an isosceles triangle of base 16 inches and edges z, and assume that z is a function of…

A: Base of triangle = 16in  Edges = z in

Exponential Growth Model

The relation that represents an exponential function is: