Use linear approximation, i.e. the tangent line, to approximate V64.4 as follows: Let f(x) Vx. The equation of the tangent line to f(x) at x 64 can be written in the form y = mx + b where m is: and where b is: Using this, we find our approximation for v64.4 is

Q: Find the differentiation and provide complete solution. a. f(x)=x/∛x2+4 b. y=(3x-1/x2+3)2

A: To differentiate: (a) f(x)=xx2/3+4. (b) y=3x-1x2+32.

Q: find the indicated derivatives. dz/dwif z = 1√w2 - 1

A: We need to find the derivative of the given z-function

Q: Find the derivative of the following, using first principles a) 2x2 b) x3 c) 8-x2

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=sin(2x)+17 To find: f'π2 and f'(π)

Q: C = C₁ ( √ ( 1² + 54²2)) + C₂ (√(K-150)² +54²)) 6

A:

Q: Please answer this NEATLY, COMPLETELY, and CORRECTLY for an UPVOTE. Find up until the second…

A: Please refer to the image below

Q: Given the function z = x²y. a. Find the directional derivative of zat (1,4) in the direction making…

A: The given function is, z=x2y at point (1,4) Angle π4. To find the directional derivative can be…

Q: Find an equation of the tangent line to the curve at the given point. y = In(x27x + 1), (7,0) y =

A: To find an equation of the tangent line to the curve at the given point:

Q: 2. Determine the derivative of g(t) = 8°[(2t + 1)² + t].

A: Given that     g(t) = 8t[(2t+1)2+t]

Q: 2. Use first principles to find the derivative of each. f(x) = √√2x − 1 a) b) y = x₁

A:

Q: Find the standard (slope-intercept form) equation of the tangent line to the following functions at…

A:

Q: Differentiate f and find the domain of f. (Enter the domain in interval notation.) f(x) = ln(x² −…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find an equation of the tangent line to the given curve at the specified point. x2 (1, 0) x2 + x + 1

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 14x – 60x? – læ + 3)dx…

A: Since you have posted a multiple question according to guildlines I will solve first  question for…

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: