1. Given the function f (x) = 4x³ + 3x² – 6x + 7. a) Determine f'(x). 2. Solve the equation algebraically: 3* = 243 3. Determine the equation of the tangent for the following function at the point of tangency (1, f(1)): f(x) = x3 – x + 4 4. Consider the graph of a polynomial function below. Y 2 1 -2 -1 3 -1 -2 a) State the domain and range of the graph.

Q: Differentiate the function f(x) +5r DO NOT simplify or factor %3D (7-z)31 quotient 012 Your answer…

A: We have to find derivative

Q: Find a cubic function y = ax³ + bx² + cx + d whose graph has horizontal tangents at the points (-2,…

A:

Q: Use a formula to express y as a function of t if y = 6x + 4x and x = t- 1.

A:

Q: Suppose that y = 2x - 5 and y = -3x + 7 are the equations of the tangents to the curves y = f(x) and…

A: We use product rule to find slope

Q: Find f′(x) for the function: (a) ​f(x)= 3w^9-7w/5w (b) f(x)= 3x-5/x-5

A: (b). According to the question, we have to find f'x for the function fx=3x-5x-5. The derivative of a…

Q: f(x) = x3 -3x2 - 3x +1 x=-1 is a root of the function how would you show that?

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Q: 9.) What is the smallest slope of the function y=x²-3x² + 5x-1 on ?

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Q: Find the point on the graph of f(x)=4−x2 that is closest to the point (0,1).

A: To find the point on the graph of fx=4-x2 that is closest to the point (0,1)

Q: 3a) Determine the equation of the tangent to f(x) = In(3x + 4), at x = 2. %3D Equation of Tangent:…

A: Please see the explanation below

Q: 9. Find the slope of f(x) = (x+2)2 +5 at the point (3,-4)

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