For a function g(x). g"(3) = -8 indicates that G(x) is at x=3 a) concave up

Q: Find the interval on which the graph of f(x)=ln(x^2+1) is concave upward ?

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Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: Find the derivative of a function at a certain number using the formula f(x) – f(x1) x-X1 x- x1…

A: Here's the solution, please have a look at it...

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

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Q: The function f(x) is defined by f(x) =2. What points (x, y) on the graph of f(x) have the property…

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Q: Find a function f such that f (x) = 2x3 and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A: Key point used: The slope m, of the tangent to f(x) at point h,k, is equal to f'x=h. Given:Eq of…

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

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

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

A: Differentiate the function fx=xx2+1 with respect to x, to obtain f'(x) and f''(x).…

Q: Let f(x)=x² – 3x'. For what value(s) of x in [–1, 1] is the slope of the line tangent to the graph…

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Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = -4 is y = 5x…

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Q: Find the slope of the line tangent to h(x) = f(x)g(x) at x = 6, given that the line tangent to the…

A: We have to find

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x<03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

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: The function g is difirentiable and satisfies g(-1)=4 and g'(-1)=2. what is the approximation of…

A: given g(-1)=4 and g'(-1)=2.         g(-1.2)=?

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: Fill in each blank so that the resulting statement is true.

A: The slope of the tangent at a point on the curve is equal to the value of the derivative of the…

Q: Find a function f such that f'(x) = 2x³ and the line 54x + y = 0 is tangent to the graph of f. f(x)…

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Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: am having trouble finding the equation of the line tangent to the graph of f at (1,1), where f is…

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Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: 2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D…

A: Given that, f(x)=x2ln x +1 To find f''(1) when h=0.2 Using second derivative formula,…

Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: Let f(x) = 4x3 + + 2Vx – 7. Find f'(x). 15. Find an equation for the tangent line to the graph of…

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Q: Find the values of a and b so that f will be differentiable at x = 3.

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Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = –2 is y = 2x…

A: Note that the slope of the line y=2x-2 is 2. Given that the tangent line to the graph of y=gx at…

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

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Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: Use the definition of the derivative to find: f(x)= 1/x^3 g(z)= z^4 - 8z^2

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

Q: For the function given by g (x) = x2 + 2x +1, use the limit definition of the derivative to compute…

A: Please refer the attached image for complete solution.

Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To find a linearization at a suitable chosen integral near a= 0.11 at which the below function and…

Q: Let f(x) = 9 – x² The slope of the tangent line to the graph of f(x) at the point (-3,0) is The…

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Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Let f(x) = 21 – x² The slope of the tangent line to the graph of f(x) || at the point (-4, 5) is The…

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Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

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Q: Let g be a function that has derivative x(x – 3) (x – 5)e2" g'(x) = Does x=3 belong to a local…

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Q: Find ☆ f'(x) using using derivative rules. f(x) =Dx+ 2 to 11

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Q: 2- By using mumerical approximation ,the value of the derivative (f'(x)) in the table is true f(x)…

A: To find the derivative.

Q: 9. If f(5) = 13, f' is continuous, and f'(x) dx = 16, what is the value of f(6)?

A: Use property of definite integration

Q: For the function f(x,y)= x^2 +2y^2 Use the first derivative test to determine if the function is…

A: Given function

Q: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…

A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…

Q: Use the second derivative to determine f"(3) for the function f(x) = x² In (x) 2ln(3) +2 O 3ln(2) +3…

A: topic - derivatives

Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a

Q: Find the x-value for all relative extrema of f(x) using the first derivative test. 1+x + x² f(x) =…

A: Given: The function is  fx=1+x+x2x2+x-2   To determine: The x value for all relative extrema of f(x)…