Given the function f(x) = x'e2a, Determine the open interval(s) where the function is concave up Determine the open interval(s) where the function is concave down Determine any points of inflection.

Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given…

Q: find the derivative of y with respect to the appropriatevariable. y = sin-1 3/t2

A: We differentiate with respect to t using chain rule.

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: The derivative with respect to X .2 y = x sin-'x + V1 – x²

A: Given:               y=x sin-1x+1-x2 Differentiate with respect to x           ddxy=ddxx sin-1x+1-x2…

Q: Find the tangent line to the function f (x) = x² – 4x + 5 at the point (3,2).

A: To find: The tangent line to function fx=x2-4x+5 at the point 3,2. Formula used: The slope of…

Q: f(x)

A: We will find the equation of tangent.

Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: Find all value of x=c, so that the tangent line to the graph of f(x) at (c,f(c)) will be horizontal…

A:

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

A:

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

A:

Q: Find the slope of the line tangent to the curve x + sin(y-π) = 2x3 + ey at thr point (-1,0).

A: Find dy/dx

Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

A:

Q: or x>0, determine the deriva

A: Consider the given function: Here the objective is to find the derivative of a given function using…

Q: Find an equation of the tangent line to f(x) = x° – 2x +1 at the point (0, 1).

A: The given function is: f(x)=x3-2x+1

Q: Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 3ex+7 f(x)= ?

A: Given:

Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

A:

Q: b. Find the equation of tangent line to the curve of function f (x) at given point: y = In(x² – 4x +…

A: We have to find the slope of tangent first.

Q: Use three-point midpoint formula to evaluate the first derivative of y=x2+5x−1y=x2+5x−1 at x=0x=0…

A: Given function is y=x2+5x−1. We have to evaluate the first derivative of y=x2+5x−1 at x=0 using a…

Q: Find the derivative of y with respect te X /3 %3D

A: Finding dy/dx

Q: on the chain rule find the tangent line to graph y=(x+2/x+1)^2, at x=0

A: We have to find tangent line to y , first we will find  value of y at x=0.

Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

A:

Q: Find the derivative for x+1 a)f(x)=- x-4 b)f(x)= sin' 2x Show the work on your notebook, take a…

A: (a) To find: The derivative of fx=x+1x2-4. Formula used: Quotient rule of derivative:…

Q: Find the derivative of the function f(x) = VI+4 using the limit process.

A: we have to find the derivative

Q: Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy…

A: Y'= ?

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 (x2 + 1), x > 0

A: Given that, y=csc-1x2+1

Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

A:

Q: To begin with, calculate the first derivative f'(x) = Now use this derivative to find the critical…

A:

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

A:

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+V3 2V3 At the…

A:

Q: Find the equation of the tangent line to the function f(x)=2x2-x  at the point where x=−1. Give your…

A:

Q: Find all x-values where f(x) = (x² + 2x – 3)4 has a horizontal tangent line.

A: We find f ' (x) using the chain rule and the power rule. f(x)=(x2+2x-3)4…

Q: Find the derivative of f(x) and solve for x sinx a. f(x) X = 6. b. f(x) e* sinx X = 0 COSX c. f(x) X…

A: Given: (1) f(x) = sin x / x  at x = π/6  (2).  f(x) = ex sinx at  x= 0 (3).  f(x) =  cos x / ex   at…

Q: 3. Find the equation of tangent line of the function f (x) = e" /x at the point æ 1. Write in the…

A: Given,  The function   fx = exx   We have to find the equation of the tangent line at the point x =…

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: The point on the graph of f(x) = 1 where the tangent line is parallel to the line 3z + y = 1 is: %3D

A:

Q: The derivative of xª at x = e is equal to .Soloot ono

A:

Q: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

A:

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: The 60th derivative of x with respect to y of y = x^60 is 60!x

A:

Q: 2. tanh-'x + lny1 – x²

A: We have to find derivative

Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

A:

Q: Find the derivative of the function. h(x) = x² arctan(8x)

A:

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A: