If f(c) is a relative extremum value, what can be concluded about f'(c)? A. f'(c) = 0 B. f'(c) > 0 If h is a strictly decreasing function, what can be concluded about h(-1) and h(1)? A. h(-1) > h(1) B. h(-1) < h(1) C. f'(c) < 0 D. f'(c) does not exist C. h(-1) = h(1) D. h(-1) = -h(1)

Q: Find y as a function of a if y" – 8y" + 15y/ = 8e", y(0) = 28, y(0) = 14, y"(0) = 12. y(x) =…

A: We have to find the solution of differential equation.

Q: - For the following graphical representation of a function f(x): (1) Mark the points on the graph…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: -2x² √4-x² O(-∞, -√2) and (√2,00) O[-2, -√2) and (√2, 2] Given f'(x)= O(-2,2) O(-√2, √21 determine…

A: Function increasing and decreasing.

Q: h' (2) = 4, then f'(2) = ? We know the following 5. Suppose that f(h) and h(r) are functions such…

A: Using the given value we find the composition function value and value of f’(2)

Q: 3. When is the function increasing and when is it decreasing? f(z) = re==z3)? xe 2 f(x)=xe 4X2)

A: Solution:

Q: What type of discontinuity is in the function f(x) = x-4/(x)^1/2 -(2)? Where is this discontinuty…

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Q: If f(q)  = 50 + 50q gives profit when selling q units, and g(t) = t^2 - 12t + 1 gives the quantity…

A: Given: f ( q ) = 50 + 50 q , where f ( q )  is the profit on selling q units. g ( t ) = t 2 – 12 t +…

Q: The function f is given by f(x) =-2 – ;e™.What is the equation of the line tangent to the graph of f…

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Q: The following graph corresponds to f"(x), the second derivative of f(x). If the graph does not…

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Q: 6. Apply the First-Derivative Test, to identify all relative extrema of f(x) = x3- Answe homev 16…

A: Given query is to find the relative extrime.

Q: 1. (a) For the function f(x)=x* - x² (whose %3| | graph is shown) use the power rule to take…

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Q: If find f'(x). ƒ'(x) = | Find f'(4). ƒ'(4) = f(x) = = 7-x² 8+x²

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Q: If f'(x) = (2-2x)e(1-x), which of the following statements is true about the graph of f(x)? Select…

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Q: Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient…

A: We can solve as follows Do not confuse in round bracket and close bracket. They are same in this…

Q: Q3. Derive the following formula for approximating the derivative f": ƒ™" (x) ≈ (f(x +3h) − 3f (x +…

A: To Derive: f'''(x)≈1h3f(x+3h)-3f(x+2h)+3f(x+h)-f(x). To find: Big-Oh error term from the above…

Q: ļim (* +4)- ƒ(x) 3. Find the derivative of the following functions using the Show all your steps. a.…

A: f'(x)=lim(h tends to 0) {f(x+h)-f(x)}/h use this for derivative

Q: Let be a function whose derivative graph is shown below. Use the graph to answer the following…

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Q: 2 7. Evaluate f' (-1) for f(x) =- x X3

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Q: Explain in your own words, how do you find the followings using first and second derivatives of…

A: To Explain: How can we find followings using first and second derivatives of function f(x):(a)…

Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: If f(x) = (3x + 8), find f'(x). %3D Find f'(1).

A: Note some formule:

Q: Let f'(x) = x³ - 9x² +24x +3.

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Q: a) y = -5x6 b) y = 6x2 c) f(x) = -7

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Q: a) f(x)=x44 b) g(x)=(3-x+4x²)(2x²- c) h(x) = x² – 3x 2-x²

A: ddxxn=nxn-1 ddxfxgx=gxf'x-fxgxgx2 [As per the guidelines I am answering only first 3 parts of the…

Q: f(x) g(x) h(x) = ;a = 3 f(x) f'(x) g(x) g'(x) 0. 2 0. 2. -1 3. 7. -7 7. h'(a) = %3D 3, 2. 2. 5. 2.…

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Q: hen f has points of inflection when x =

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Q: p(x) = (-2x)f(x), q(x)= f(g(x)), r(x)= 31 Use the table to find the derivative values. f(x) %3D

A: