y = f'(x) 3. 2 14 -4 -3 -1 1 2 3 4 5 (3, –0.5) -14 (1, –0.5) -2 (4, –2) -3. (5, –3) -4

Q: Suppose that f(x)=(x+2)(x-2)^2. (G) Use interval notation to indicate where f(x) is concave down.…

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Q: V7x* +4x' -x² -2 lim x³ - 2x² -3x+1 4x-x²-2 x -0

A: Solution:

Q: For what value of k will the function f be continuous on (-, ∞)? x2 - 81 if x + -9 f(x) = X + 9 k if…

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Q: Suppose that f is a function given as f(x) = -3x² - 2x - 3. Simplify the expression f(x + h). f(x +…

A: f(x)=-3x2-2x-3(i) f(x+h)=-3(x+h)2-2(x+h)-3

Q: 1 show that f (-2) = f(2). 4 If ƒ(x) = x" 4

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Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the…

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Q: 5. If f(x) = 2 x + 3 a) f-¹(g(x)) and g(x) = 21, find b) the domain and range of f-¹(g(x))

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Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

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Q: Sketch the graph of f(x) = x2 - 9, x =< 4 f(x) = 8x - 25, x =< 4 Is f(x) continuous at x=4?…

A: To check: Whether the functions f(x) = x2 - 9, x≤4 and f(x) = 8x - 25, x≤4or not. . Solution: Sketch…

Q: Let g(x,y)=y−6/(x+2)^2 Indicate the range of g using interval notation

A: To find the range of the below function. gx,y=y−6x+22

Q: Apply the limit definition to find the derivative of the function, f(x)=2x²-5x+9. Not the short cut…

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Q: For the function f(x) = 4x? +16x + 25, find f'(x) using the definition f(x+ h) - f(x) lim h-0

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Q: Point (x, y) is on the graph of f(x). Determine the corresponding point on the graph of f-'(x).…

A: The inverse of a function y= f(x) tells about the value of y for certain x Similarly, inverse…