Find the points on the graph of f where the tangent line is horizontal. tangent line is 3x^2-16 (derivative of  x^3-8x^2)   x= 0, 16/3   smaller value (x,y)= larger value (x,y)=

Q: Explain how to apply the First Derivative Test.

A: Explain how to apply the First Derivative Test.

Q: Evaluate the second derivative at this critical number.

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Q: Determine the derivative of f(x) = Cosh(5 x) csc(x)

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Q: Find the derivative of the given function. Infsech(x) + tanh(x)) 1) sechx+tanhr sinhx+1 sechx-tanhx…

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Q: Find the derivative. Simplify where possible. y  = Cosh-1 √x

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Q: What are the the mean value theorem in application of derivatives?

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Q: Describe the First Derivative Theorem for Local Extreme Values?

A: Describe the First Derivative Theorem for Local Extreme Values?

Q: Find the slope of the tangent line to the curve y- x + 4=0 at the points (8, 2) and (8, -2) in two…

A: We will find out the required solution.

Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: why first derivative is zero at local maximum and local minimum of function in an open interval

A: The first derivative is zero at local maximum and local minimum of function in an open interval…

Q: The second derivative of function: Inesina will be Select one: O sina O -sinz

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Q: Find the derivative. Simplify where possible.  f(x)= ex cosh x

A: Given function is

Q: Estimate the slope of the tangent line at the point x = 3, for f(x) = In(x). (Use decimal notation.…

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Q: Find the derivative. Simplify where possible.

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Q: 23. The slope of the tangent line indicates the rate of change of the function, also called the 24.…

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

Q: Find the approximate derivative for f(x) = cos x on the interval [-7, 1] using forward difference…

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Q: b) Trapezoidal rule with end corrections using the first derivative

A: The formula for the trapezoidal rule with end correction is in the integral with upper limit is a…

Q: An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A: We will estimate the volume of cylindrical metal as following. Inside radius = 2 cm Inside height =…

Q: Please help. *Find the slope of the tangent line to the given curve below at (5,3). y² - 2x + 5=0.…

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Q: 3 + 2x +5

A: GIVENy=x3+2x+5   and x=2

Q: Explain in 200 words the relationship between the secant line, slope of the tangent line, derivative…

A: Given: secant line, slope of the tangent line, derivative of a function using the limit process,…

Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Are critical numbers from the first derivative used in the test for concavity?

A: We have to tell that  critical numbers from the first derivative used in the test for concavity or…

Q: Compute the derivative using derivative rules that have been introduced so far y = ex-12

A: To differentiate y=ex-12, with respect to x, apply the exponential rule of differentiation,…

Q: Estimate the slope of the tangent line to f(x) = tan (x) at the point x = 4 (Use decimal notation.…

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Q: This is determined by the largest derivative, or the highest level of differentiation, present in a…

A: We have to check

Q: Brd Derivative OF y=-Jin3x

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Q: calculate the derivative y = ecosh−1 x

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…

Q: Explain the relationships among the slope of a tangent line, theinstantaneous rate of change, and…

A: The slope of a tangent line of f on x is,msec=f(x)-f(a)x-a

Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: (c) Trapezoidal rule with end corrections using the first derivative and third derivatives

A: The given integral is ∫abf(x)dx=∫-11e-x2dx So, a=-1, b=1, f(x)=e-x2 c) We have to find the…

Q: Find the derivative of the cotangent function y=cotx

A:

Q: Explain how the Second Derivative Test is used.

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: Find the general anti-derivative of f(x) = 3. + Vx on a continuous interval. Please select file(s)…

A: topic - integration

Q: 1. Describe the relationship between the derivative of a function to the slope of the tangent line.

A: Query- Describe the relationship between the derivative of a function to the slope of the tangent…

Q: Can the  derivative of f(x) be zero in the interval [-1,0]

A: Given, fx = x4+8x+3  f'x = 4x3+3   We have to find the derivative of fx be zero in the interval -1,0…

Q: Estimate the slope of the tangent line of the function f(x) = 7e* at the point x = e. (Use decimal…

A: We find f'(x)

Q: Find the first derivative of y = (In x)"

A: The differentiation of nested form of function is calculated using the chain rule of…

Q: What is the relationship between the secant line, slope of the tangent line, derivative of a…

A: Solved below

Q: Use LONG METHOD DERIVATIVES to find the slope of the tangent line to the curve: f (x) = V7x at point…

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Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

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Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

Q: Find the slope of the tangent line to the curve y-x+5 0 at the points (6, 1) and (6,-1) in two ways:…

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Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e'. =-e?. Equation:

A: As we know that the equation of the tangent line is: y-y1=mx-x1 Where 'm' is the slope. Given:…

Q: Find the derivative of f(x) = 3/x at x = 3 by using the definition of derivative. Note that you will…

A: Given,f(x) = 3x at x = 3

Q: Find the derivative of using first principle?

A: we have to find first derivative of y by using first princple

Q: Find the derivative of the function at Po in the direction of A. txу) - - ху + у, Р,(10, - 2),…

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Q: Find the derivative of the function. Simplify wherepossible  x lnarctan x

A: Let f(x)=xlnarctanxDerivative formula:ddxlnx=1xddxtan-1x=11+x2arctanx=tan-1x