h. Use the second derivative to identify intervals where f(x) is concave up. i. Use the second derivative to identify intervals where f(x) is concave down. j. Use the second derivative to find any inflection points. -1/2

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

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Q: Use the Quotient Rule to find the derivative of the function. Re) = Sos(t) f'(t) =

A: We will find the derivative of the function f(t) as following.

Q: For f(x) = x3, show that the slope of the secant line over [l,x] is x 2 + x + 1, and use this to…

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Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The derivative gives the rate of change of a function. It gives the slope of the function at a point…

Q: D At f(x)= x²+x -6, At which values of x does he graph of f(x) have a horizontal tangent line

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Q: Find the (a) true error and (b) relative error of the following: The derivative of f(x) = 2−x at x…

A: For the solution follow the next step.

Q: Let f(x)=1.91.9x. Estimate the derivative f′(1.1) to within two decimal places by using a small…

A: The given function is f(x) = 1.91.9x.

Q: Let f(x) = x* – 2x + 14. Then the equation of the tangent line to the graph of f(x) at the point (1,…

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Q: # 41) Use the definition of derivative to find f(r) and "(r) for (r)= 1+ 4r- r

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Q: compute the derivative indicated. Find a function such that ∂f/∂x = 2xy and ∂f/∂y = x2.

A: ∂f∂x=2xy∂f∂y=x2

Q: Differentiate the following function:R(q)=q^4−9lnqEnter the derivative here:

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Q5:- Find the first order derivative of each of the following functions: c) ysecx = x(secy) %3D

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Q: For which values of x does f(x) = 3ex 6x have a horizontal tangent line?

A: Let's find.

Q: V. Find the third derivative q = tsecv0.2t" +1 Where r is the last digit of your university ID.

A: It is given that: qt=tsec0.2t4+1 Let u=0.2t4+1 qt=tsecu Differentiate w.r.t t to get:…

Q: 3x²+1 e) у %3D cos?(3x?) f) y = x-2

A: We need to evaluate the derivative of the following function e y = cos23x2f y = 3x2+1x-1

Q: ƒ(x) = 1/x + 2

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Q: Use the second derivative test to find the local extrema for the function f(x,y) = x² +y³ + 2xy – 3x…

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Q: Find f'(x) and the value(s) of x where the tangent line is horizontal. f(x)= x/(5x-9)^3

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Find the point(s) on the graph of f where the tangent line is horizontal. (If an answer does not…

A:

Q: Given

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Q: b) f(x) = xe

A: If f(x) is a function of x and the second derivative of f(x) exist at any stationary point x0.1.If…

Q: Let f be the function given by f (x) = 3*. For what value of x is the slope of the tangent line to…

A: Given, fx = 3x  We have to find the value of x at which the slope of the tangent line to the curve…

Q: 2. y = 1 (tanh~' 2x)3

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Q: Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist,…

A: f(x)=(x+5)23  f'(x)=23(x+5)-13  f'(x)=23 (x+5)3Let's understand f'(x) as a different…

Q: Consider f(x) and g(x) = 3f(x) + 5.  Compare the slope of the tangent line to f(x) with the slope of…

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Q: Find the point(s) on the graph of f where the tangent line is horizontal. (If an answer does not…

A: Given f(x) = xx2+81Since slope of tangent at any point on curve is given by derivative of f(x) at…

Q: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

Q: Let f(z) = z – 6z. Calculate the difference quotient (3+h)-{(3) - for h = .1 h = .01 h = -.01 h = -1…

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Q: Use the definition of the derivative to find the derivative of the function f(x) = v2x + 1, then…

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Q: Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist,…

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Q: Let f(x) = 3x^2 + x + 5. a) Find the equation of the tangent line at x = 10. b) For what value of x…

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Q: Use the Quotient Rule to calculate the derivative for the function g(t) = +4 at t = 1.

A: Given : gt = t4+4t4-4

Q: Find the (a) true error and (b) relative error of the following: 1. The derivative of f(x) = x3 +…

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Q: Q15: Find the derivative: f(x) = (In x)?

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Q: Given the function y = f(x) = /x² + 1 a. Use the first derivative to find the intervals

A: The function is given y=fx=x2+1. a To find increasing or decreasing function. y=x2+1 Take the first…

Q: Use the fact that derivative of a function at a point is the slope of the tangent line to the graph…

A: We know that the derivative is 0  at the maximum and minimum point on the graph  From the graph we…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. (If an…

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Q: Use the product rule, quotient rule, and chain rules to find the derivative   f(x)=sec(x^2)/e^x

A: on differentiation we get the value

Q: d'y of y = r10 sec 2

A: y = x10 - sec x Differentiating with respect to "x" dxdy = 10x9 - sec x tan x Again, Differentiating…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: zチー1 メニ」t

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Q: a) Determine the derivative, y (x) for the composite function below. g(x) ]V y(x) =

A: Equation of normal line

Q: 4) Determine f(x) = co the point where the slope of the tangent is 0 for the function 0<x< 2π

A: The derivative of a function has a wide application. The most important application of differential…

Q: Find the point(s) on the graph of f where the tangent line is horizontal. (If an answer does not…

A: We have given function fx=xx2+9 We have to find out the points where the tangent line is horizontal…

Q: Find the slope of the line tangent to the graph of f(x) = -x-1 at x = -3. Provide your answer below:…

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Q: Use the limit definition to compute the derivative of the function at  t = 3.   f(t)= t-3t2   f…

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Q: Using the definition of the derivative, find f (x), if f(x)=mx+b where m,b are real.

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Q: C45 O Use the first derivative test to find the local extrema of f(x) where f(x) = 4x3 - 36x.

A: (A)- local maximum at - root(3) and minimum at root(3)