a. Find the local extrema of the function f(x)=csc^2(x)−(2/√3)cotx on the interval 0

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

A:

Q: 8. Suppose the derivative of the function y = f(x) is y' = (x – 1)*(x – 2)(x – 4). At what points,…

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Q: Find the derivative of the function at the given number. f(x) = 3 – 4x + x², at -1 %3D f'(-1) = %3D

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 1) cos (x²). If f(1) = 1, what is the…

A:

Q: a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent…

A: Given: fx=x2-5x To Find: a. f'x=?b. Slope of tangent line of the given function at x=-1 and x=3

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: find the function with the given derivative whosegraph passes through the point P. ƒ'(x) = 2x - 1,…

A:

Q: Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics…

A: The concentration is given as , Ct=e-αt-e-βtβ-α where α and β are constants with β > α > 0.

Q: Your job is to estimate this special base. In other words, estimate the value of b for which, at…

A:

Q: In x se the second derivative test to find the local extrema for the function f (x) = x3 •

A:

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 5s

A:

Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: Use the definition of a derivative to determine all points for the function f(x) = ((x+|x|)^2)+1 is…

A:

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Use the first derivative test to find where the local extrema are on the function f (x) = x³ + 6…

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Q: Find the derivative of the function f(x) = coth−1(x2)

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Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Let f(x) be a function that is differentiable at x = -2. Given that f'(-2) = 3 and f(-2) = 6, find…

A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

Q: Let f be the function given by f(x) = 4x¹. What is the approximation for f(1.15) found by using the…

A: The answer is given below:

Q: 2. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

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Q: g(u) u +1

A:

Q: (a) Let f(x)=√√2x+1. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A:

Q: 6. Sketch the graph of y= x2+ by using the properties of the derivative.

A: The given function y=x2+2x

Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

A:

Q: Find the derivative of the following functions using the long method (limits) y= tan x

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

Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

A:

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: The graph of a function is shown together with the tangent line at a point P. 10 9. 8. 7 6. 4. 3 2 1…

A: Here from Graph Red line tangent to given function f at point p  so derivative of f is equal to…

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: Find the x-value for all relative extrema of f(x) using the first derivative test, and specify…

A: f(x)=x3/3 + x2/2 -2x Find the x-value for all relative extrema of f(x) using the first derivative…

Q: 7. Consider the function f(x) X - 3 a. Using the definition of the derivative at a point, calculate…

A: Given : f(x) = x / x - 3   (1) f' (2)  (2) tangent line when x = 2 (3) normal line when x = 2

Q: In our last class discussion we found that a function y(x)= x* indicated by taking y"(x) = 0 that…

A: Definition: The first derivative of a one-variable function is zero at the points called stationary…

Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

A:

Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: 3- Suppose that the second derivative of the function y = f(x) is y" = (x + 1)(x - 2). For what…

A: 1)y'' = (x+1)(x-2)2)y' = (x-1)2(x-2)(x-4)

Q: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Find the derivative of f(x) = cot^−1(x^2 + 3)

A:

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: 24. Consider the graph of y = Use limits and 1+ eax first derivatives to determine how the shape of…

A:

Q: 2. (a) Demonstrate the method of the limit definition of derivative to find the derivative of f(x) =…

A: Limit of differentiation

Q: Find the derivative of the transcendental function. y = ex - cot x y' =

A: derivative of ex = ex dderivative of cot(x) = - cosec2(x)