Given f(x) = 3x² – 3x + 2, find f'(x) using the limit definition of the derivative. f(x + h) = ở 3(2+h) −3(2+h)+2 6xh+3h²3h f(x+h)-f(x) = f(x+h)- -f(x) h f'(x) = lim h→0 f(x+h)-f(x) h = 0 6x +3h-3 6x - 3

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A: f(x)=-(x-1)2 = - (x2 - 2x + 1) = 2x - x2 - 1

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Q: Compute f’(-2) using shortcut rules. f(x) = 5x + 9

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Q: Differentiate the function f. Use the form f'(x) = f(x) = 9x² + x + 8 f'(x) = = lim h→0 f(x +h)-f(x)…

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Q: Find the limit of the function as x approaches −1.x^2−4x−5x/x+1limx(→−1)f(x)=

A: Given,

Q: Compute the derivative of f(a) the limit definitions. rf from the limit definition. Note: you can…

A: The given function is:fx=x23

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: Let f(x)=-3x²+2x-7. Use the limit definition of the derivative (or the four-step process) to find…

A: Limit definition of derivative of a function f(x) is given by f'(x)=limh→0f(x+h)-f(x)x+h-x

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: a) f(x) = x + √2x − 1

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Q: Let f(x) = x³ + 3x² - 24x + 25. (a) Use the definition of a derivative or the derivative rules to…

A: Given function is fx=x3+3x2−24x+25. a Differentiate fx=x3+3x2−24x+25 with respect to x…