Describe the process of linearization of a function f(x) at a point x = a, and explain how it can be used to approximate the function value at a point P with x-value different than x = a.

Q: The derivative of . f(x) = Vx4 is %3D

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Q: Find the slope of the secant line to the function f(x)=x3 when x=1 and x=2.

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Q: Sketch the graph of a smooth function ƒ and label a point P(a, ƒ(a)) on the curve. Draw the line…

A: The aim is to find the graph of a smooth function and represent the line which shows the linear…

Q: Tell whether the enumerated function is linearly dependent or linearly independent using wronskian.

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Q: Differentiate the function.      f(x)  =        ______1______                            In x

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Q: The derivative of f(x) =3 4 is %3D

A: Consider the given function, fx=4x5 The property of derivative is defined as, ddxxn=nxn-1 Convert…

Q: Find the derivative of the function 2t5 + t2 -5 h (t) = %3D t2 h'(t) = 6t2 – 10t-3 h'(t) = 6t-2 +…

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Q: 4 f(x) = x +

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Q: Determine the derivative of a quadratic function of general form y=ax2+bx+c.

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Q: Find the linearization of the function F(X) =sqrt (x+3) at a= 1 and use it to approximate the…

A: Therefore linearization at a = 1 is,

Q: Use the definition to compute the derivative of the function f (x) = Vx2 + 1.

A: We have to find derivative

Q: Determine the local extrema of the function f(x)=x2lnx.

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Q: Use the Chain Rule to find the derivative of the function. y = (2x2 − 3)3 y' =

A: The chain rule to find the derivation is,

Q: What does it mean for a function to be right-continuous at a point?

A: A function f is right continuous at a point c if it is defined on an interval [c, d] lying to the…

Q: .Find the Global Extrema for f(x) = Bx4-BeB-A)x. Use the second derivative to determine if those…

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Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

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Q: Differentiate ex with respect to x, assuming that y is implicitly a function of x.

A: Here we have to use the concept of implicit derivative

Q: Differentiate the function. f(x) = e2 f'(x)

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Q: Find the derivatives of the functions in Exercise

A: The given function is y=x-35+π32

Q: Use the Chain Rule to find the derivative. f(x) = (x5 – x3 – 1)2/5 %3D

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs.

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Q: Find the average rate of change of the function from X1 to X2 f(x)= -3x2-x  from X1= 5 to X2= 6

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Q: y = V4x3 –6

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Q: What does it mean for a function to be left-continuous at a point?

A: function to be left-continuous at a point?

Q: Let f(x) = }x² – x³. Find the value(s) of x if the second derivative f" (x) equals zero.

A: Use the formula, ddx(xn)=nxn-1 to calculate the derivative. Differentiate f(x) with respect to x to…

Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

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Q: Let f and g be the functions defined for x > 0 by f(x) = (Væ)* and g(x) = (Vx)** Which function is…

A: According to the given information, Consider the function f and g defined as:

Q: Differentiate the function.

A: we have bee given the equation  u=t23+2t3 it can be written as  u=t21/3+2t3

Q: Differentiate the function. h(x) = In(x + V - 12

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval.

A: Given ,y = Cos x - Sin x      0,2πf(x) = Cos x - Sin x

Q: Consider the function f(x)=2√(x)+3 on the interval [4,5]. Find the average or mean slope of the…

A: The mean slope is given by: f(5)-f(4)5-4=f(5)-f(4)1=f(5)-f(4)

Q: Find the average rate of change of the function f(x)=x2+6x from x1=5 to x2=9.

A: To Find the average rate of change of the function f(x)=x2+6x from x1=5 to x2=9

Q: Find the derivative of the function. f(x) = 5x4 - x6 f'(x) = %3D

A: The given function is                                   f(x)=5x4-x6 Now we find the derivative of…

Q: Find the derivative of the algebraic function. f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)

A: Given information: fx=x3-xx2+2x2+x-1

Q: Differentiate the function. g(x) = In(xe-Sx)

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Q: Consider the function f(x) = 2x interval - 2, 2|. Find the average or mean slope of the function on…

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Q: Find the derivative of the function. f(x)% 3D(x²+1)(x² + 10)/3 f'(x)%3D

A: Given equation

Q: Find the derivative of the function. f(x) = V3 - 6x2 %3D f'(x) = || %3D

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Q: Write an expression for the linearization of f at a

A: Given:Linearization of  f at a

Q: Let f(x) = x-3 Use the definition of derivative to find f'(x). %3D 2C

A: Given : fx = xx-3

Q: f(x) = x3+x

A:

Q: sketch the curve f(x)= ln((x^2-4)/(x^2-3x-4))

A: given curve is                                                     f(x)=lnx2-4x2-3x-4 we have to…

Q: Find the average rate of change of the function:f(x) = x2 + 2x from x1 = 3 to x2 = 5

A: Given function is fx=x2+2x. To find: The average rate of change of the given function from x1=3 to…

Q: What do all members of the family of linear functions f(x) = 1+m(x+3)have in common? Sketch…

A: Given: The linear function, fx=1+mx+3.

Q: Differentiate the function y=(1−x)3 without using the chain rule.

A: Differentiation: y=(1-x)3 y=1-3x+3x2+x3ddx(xn)=nxn-1

Q: Calculate the derivative of the function. f(x) = V7x + x2 f'(x) =

A: Explanation of the solution is given below...