Consider a quadratic function f(x) = ax?+ bx + c, where a, b, CER and a # 0. She hat the tangent line to the graph of f at the point P(Xo.Yo) is given by y- y, = (2ar, + b)(x-,). n this item, please use the limit definition of derivative.

Q: f(x+h) – f(x), Use the definition of the derivative (that is, f'(x) = lim h0 3 = 3r2. dr to show…

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Q: Find the equation of the tangent line to the function f(x)= x^3-4x at the point where x=0. Do not…

A: Here first we find the slope using the formula m=f'0 Then equation of the tangent at point x = 0,…

Q: Find the derivative using the chain and power rules. sin3x Please justify and explain why.

A: Let y=Sin3x.

Q: Given functions f and g for which f(- 6) = 1, ƒ'( – 6) = 1, g( – 6) = 6, and g'(- 6) = 2. Evaluate…

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Q: Determine the slope of the secant line for the following function that passes through the given…

A: Topic = Functions

Q: for the function f(x)=11x^3-x, find the slope of secant line at interval [1, 1.01]

A: We have given a function f(x).

Q: a).Find x value where the graph has a horizontal tangent line. f(x) = x^3 + x Using the fact that…

A: The given function is  f(x) = x3 + x Differentiate with respect to x , we get f'(x) = 3x2 + 1

Q: Differentiate: y dy dx 11 In(x) 26

A: Let's find derivative of given both  problem.

Q: y = 4x + 10x². Determine the equation of the tangent to the function at [2, 2]

A: Solution will be given below

Q: How can the derivative function definition be applied to this problem?

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Q: Show that axlna is the derivative of ax (a>0).

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Q: Define f(x)=2x^4-3x^2 as a Maple function. Find the equation of the tangent line at the point x=2.3.…

A: We have,  fx=2x4-3x2 The derivative of fx is f'x=8x3-6x Slope of tangent line at (2,3) is f'2=8…

Q: consider the function y=5x^2+20x+10. Can you find P & Q such that the tangent lines to these points…

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Q: Computate the derivative Y= 9X V1-9x

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