Which of the following statements is TRUE? a. If f '(3) = 5 and g '(3) = 4, then the graph of f (x) – g(x) has slope of 9 at x = 3. O b. The curve y 2x3 + 4x + 5 has a tangent line with slope of 3x. c. The derivative of y 4x3 + 2x – 1 is y' = 12x² + 2. d. If f is a differentiable function at x = a, then the tangent line to the graph of f at the point (a, f (a)) is given by y + f(a) = f'(a)(x + a).

Q: If ƒ′(x) = 3x + 2, find the slope of the line tangent to the curvey = ƒ(x) at x = 1, 2, and 3.

A: Slope of the tangent line is the derivative of the given function at the given point. Therefore…

Q: In the second diagram at right, the tangent line at x = 1 has been included. Find the slope of the…

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Q: 3. Determine the slope of the tangent line to the curve f(x) = at (2x + 1)2 x = 1 by using the…

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Q: a. Determine the derivative of k(x) = (-2x* + 3x - 4)(x" – x- 1). Simplify your answer. b. What is…

A: The detailed solution is given below. Thank you

Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

Q: 1. For the function f(x) = 2x2 +7x-3, %3D (a). Find the slope of the tangent line at c = 4. (b).…

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Q: 22. Find an equation of the tangent line to the graph of f(x) = 4 - x² at (a) (-1,3); (b) (0, 4);…

A: Given: f(x)=4-x2 To Find: the equation of the tangent line to the graph at a) (-1, 3) b) (0, 4)…

Q: 16. Which of the following statements is true? A. The slope of a line can be applied for curves or…

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Q: At which x location on the graph of f(x) = -x² - 2x + 15 is the slope of the tangent 0?

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Q: 7. Find the equation of the tangent line to the curve y = - 1-3x at x =-1 using calculus and…

A: Given curve is y=21-3x At x=-1, y=21-3·-1=21+3=24=12 So, the point is -1,12

Q: If f(x)=x²-10, find an equation of the tangent to the curve passing through the point (5, 1). A. y-1…

A: Given,.Given point is (5,1).

Q: 5. Determine the slope of the tangent at point (1,5) on the graph of f(x) = (9 – x²)} + 1.

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Q: The derivative of a function at each point is itself. y=kex

A: To find out the derivative of the function.

Q: Use implicit differentiation to find the equation of the line which is tangent to the curve 2xy +…

A: Given equation: 2xy+3x2-5x=4 We know that slope of tangent will be defined by dydx-1,2

Q: Determines the equation of the tangent to the representative curve of f(x) = 2x 2 + 4x - 1 when × =…

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