68 Considering the function f:R\(0) -R./(x) = 3x+ 4x-1 a) Find the derivative f. b) Determine the gradient of the tangent to the curve, at the point (2, 8.5) c) For what values of x does the gradient of the curve equal zero? ie. solve f'(x) = 0) d) For what values of x is the function strictly increasing?

Q: Find an equation of the tangent line to the graph of the function f through the point (xo, Yo) not…

A:

Q: Using the definition, find the derivative of the function f(z)=(2z-i)/(z+2i) at z=-i.

A: The given function  is: To find the derivative of the function f(z), differentiate it with respect…

Q: Using a Derivative Let f'(t) f(5).

A: Given that f'(t) <0 in the interval (2,8).

Q: Use the definition of the derivative to find the equations of the lines described in Exercises…

A: We can use the definition of derivatives to find the equation of tangent line at any point on curve…

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Differentiate both sides of the equations. Use chain rule for differentiation.

Q: Zero directional derivative In what directions is the derivative of ƒ(x, y) = (x2 - y2) / (x2 + y2)…

A:

Q: a. Find the slope of the curve y =x° +3 at the point P(- 1,2) by finding the limiting value of the…

A:

Q: 5y4+7=x4-3y; x=3, y=-2

A: To find slope of a line tangent to the given curve at a given point. To make a sketch of this…

Q: (a) Use implicit differentiation to find an expression for (OR y') in terms of z and y. (b) Find the…

A: Differentiate y w.r.t. to x .

Q: Using the definition, calculate the derivatives of the functions inExercise Then find the values of…

A: Givenf(x)=(x-1)2+1 To find derivative of f

Q: 4) Find direction derivative f(x,y) = x2-3xy at the point (-1,2) in the direction 0 6 %3D

A: Directional derivative of a multivariate differentiable function along a given vector v at a given…

Q: 5) Determine the slope of the tangent line to the function with the given information: a. f(x, y) =…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Uncover the function f shown that the slope of the tangent line to the chart of f at any point (x,…

A:

Q: Using first principles (by definition), prove that the derivative of a constant is 0.

A:

Q: 1 Find an equation of the line tangent to the graph of f(x) = a) at (1,1); b) at c) at a) The…

A:

Q: 28. Using the method of "First Principles" and showing all steps, determine the -3 2x-1 properly…

A:

Q: II. Application of Derivatives 3. Find the tangent line to f (r) = (2– 4x²)° at z = 1.

A:

Q: Consider the function f(x)=sin⁡xcos⁡x on the interval 0≤x≤π. (a) Calculate the derivative of f. (b)…

A:

Q: Find all points (x, y) on the graph of f(x) = x? with tangent lines passing through the point (3,…

A:

Q: Using the definition, calculate the derivatives of the functions inExercise. Then find the values of…

A: The derivative of fx with respect to x is defined as:limh→0fx+h−fxh

Q: 28. F(v) V v+2

A:

Q: Finding a Second Derivative In Exercises 45-50, find d?y/dx² implicitly in terms of x and y. 45. x2…

A:

Q: 17. Applying the quotient rule, what is the correct FIRST STEP in finding the derivative of the…

A:

Q: olw) - " ir Use part one of the fundamental theorem of calculus to find the derivative of the…

A: g(w)=∫0wsin7+t5dt The fundamental theorem of calculus is ddx∫0u(x) f(t)dt=f(u(x)).ddxu(x)

Q: A. Use implicit differentiation to find the derivative: sin(xy)=x6 - y

A:

Q: Tocal maXIITum of .3 Use second derivative test, If f(x) 36x + 4 then f(r) has a local maximum at…

A:

Q: Second Derivatives Find y" in Exercises 59–64. 62. y = 9 tan (3)

A: y=9tanx3Differentiate…

Q: (b) Consider the function f(x) = x - 1. Find the average rate of change from 1 to 3, then find the…

A: The average rate of change of a function is defined by the formula . This average rate is also…

Q: Inconclusive tests Show that the Second Derivative Test is inconclusive when applied to the…

A: To show second derivative test is inconclusive.

Q: Implicit differentiation. Given: 2x+3xy+4y=24 Find in terms of x and y and the tangent line at (1,2)

A:

Q: 4- x Find the equation of the tangent line tof-l at the point P (G, 1) for f(x) = x+1 Provide your…

A: Topic:- application of derivatives

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A:

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x,y) =…

A: The Second Derivative Test:  Find the critical points of . that is the solution of the simultaneous…

Q: 1. f(x) = sin x at the point with abscissa x = A. Point of Tangency B. The Gradient of the Tangent…

A: Equation of tangent and normal

Q: Use implicit differentiation to find dy/dx 4x^2-7y+2=8y^2-5x B) Find the equation of the tangent…

A: We have to find derivative And equation of the tangent line

Q: 1 Definition of Derivatives Use the definition of the derivative to find f'(x). 1. f(r) = 3r2 – 4r +…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Uncover the function f shown that the slope of the tangent line to the chart of f at any point (x,…

A:

Q: 5. Consider the function f(1, y) = sin(r² + y²). (a) direction of (4, 3). Find the derivative of…

A: Given :-  The given function  To Determine :-  (e) The equation of the line normal to the surface…

Q: QI/Find the derivative of the function f(z, k) = z* – 16k³ + tanh(z) – 4 csc(k) in terms of z and k…

A: F is the function of two variables so we have to calculate partial derivatives

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A:

Q: Find the derivative. (The Fundamental Theorem of Calculus -- Part 1) 19) y = cos ft dt COS-

A:

Q: Definition: "The derivative of a function f with respect to the variable x evaluated at x = a is"..…

A: Answer

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: Consider the given function as y=cos3x+3cosx+79

Q: Using the definition, find the derivative of function 2z-i 1 (z)= at the point z = = -¡. z + 2i

A:

Q: How to find the antiderivative of the given derivative function? a. To find the original function.…

A: The answer is given below in the next step:

Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the…

A:

Q: Use implicit differentiation to help you find the value of the gradient for the equation x² – e =…

A: differentiate the given function with respect to x on both sides of the equation.…