1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x < 0 ax² + bx + c; 0 < x < 2 f(x) = -ax² + 1 + 5; x > 2 4

Q: (2) Find the derivative of each of the following functions (a) f(x) = (1+x*)²/3 (b) g(x) = V1+…

A: a) We use the power rule and chain rule

Q: Prove that the function f(x) = x 5 + 2x 3 + 4x − 12 cannot have two real roots. (Hint: Use the first…

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Q: 2. [4 points] Find the derivative of the following function. 1+2x f(x) 3-4x

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Q: The function g(x) = 12x2² - sin x is the first derivative of f(x). If f(0) = -2, what is the value…

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Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: 5. Consider the function f(x). f(x) = (2x² + 3x + 1 |x| sin(x - 1) + 1 if x < -1 if -1 < x < 1 if 1…

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Q: 1. Find the derivative of the following: a) 3x²+6x f(x)= 5x-1

A: according to bartleby guide line we do only first part of multiple questions…

Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. Given the function f(x) = x³ - 3x² - 9x + 7, make a sign diagram for the first derivative and…

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Q: Find the derivatives – do not simplify a. y= x4- 3square root of x + 5x2/3 +8/x-3

A: ddxxn=n xn-1

Q: Find the derivative of the following: a.) f(x) = 5x6 +- 3x3/5 x3 b.) f(x) = (x' + 4x)(x5 – 2) (Hint:…

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Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: A2) Find the derivative of the following functions: x2 + 2 (a). f(x) x2 – 2 (b). f(x) = 2 tan-1(x) –…

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