The graph of f' is shown. Find the interval(s), if any, on which f increases. y =f '(x) -2 a) O(-0, 0) b) O(-00, 3) c) Of is not increasing anywhere. d) O (-3, 0) e) O (3, 0)

Q: compute the derivative. g(x) = tanh−1(ex )

A: We have to compute the derivative of the function: gx=tanh-1 ex We know the formula of derivatives,…

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

A:

Q: Consider the function f(x) whose second derivative is f”(x) = 10x + 8sin(x) If f(0) = 2 and f’(0) =…

A:

Q: 2) Find the derivative of f(x) = tan(1+ cos 3 x) %3D

A: As the function involved function in a function we can apply chain rule and find the derivative of…

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

A:

Q: HiHtar is THe secoyd derivative OF Y

A:

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

A:

Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e". %3D Equation:

A: To find the equation of the tangent line to the graph of: y=f(x)=ln(-x) at x=x0=-e4 The equation of…

Q: Find the global maximum and minimum of the function on the given…

A:

Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

A:

Q: Consider the function f(x) whose second derivative is f''(x)=5x+3sin(x) If f(0)=2 and f'(0)=3 what…

A: Given : f''x = 5x + 3sinx

Q: Consider the function f(x) = x³ – 2x + 4 on the interval (-2, 2) with h = 0.25. Use backward,…

A: Given that fx=x3−2x+4 To use backward, forward, and central difference methods to approximate first…

Q: 54th Dorivative: fle)=2-4sin (a2)

A:

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

A:

Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of…

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Find the derivative of the function by the limit process. f(x) - f'(x) =

A: The given function is f(x)=4x2We have to find the derivative of f(x).

Q: Find the derivative of the function f(x.y) = tan -1 y at the point (4, - 4) in the direction in…

A:

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: compute the derivative g(x) = tanh−1(ex )

A:

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

A:

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

A:

Q: Compute the derivative of the function y = 6 cos- (7x) at the point x = (Use symbolic notation and…

A:

Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

A: We have to find: a. critical points of fb. On what intervals is f increasing and on what intervals…

Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

A:

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

A:

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: 2х Use the Limit to determine the derivative of f (x) Then X-1 check your result by using the…

A:

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

A:

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

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

A:

Q: Find the fourth derivative of f (z) = 3* + In (z) – 191z. Enclose arguments of functions in…

A: To find :  Fourth derivative of function ,  f(x)=3x+lnx-191x

Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: the derivative of f(x) = xi at the point x = 4?

A:

Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

A: