Problem 3
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The derivative of the function f(x) = 3(x-2)^2 + 2 is 6(x-2). The equation of the tangent line to f(x) when x is 4 is y = 18 + 6(x - 4). Given the functions f(x) = 3(x-2)^2 + 2 and g(x) = sqrt(x), the points of intersection between their tangent lines at x=2 and x=5 determine the centers of three circles with radius 5.
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![Question 3 a) Given the function: f(x) = 3(x-2)^2 + 2 , determine the derivative of the function and find the equation of the line tangent to f(x) when x is 4. b) The points of intersection between the lines tangent to g(x) when x=2 and the line tangent to f(x) when x=5 are the centers of three circles with a radius of 5. Determine the equations of the circles where g(x)= squareroot[x] .](https://image.slidesharecdn.com/problem3-090607020028-phpapp01/85/Problem-3-1-320.jpg)
Problem 3
- 1. Question 3 a) Given the function: f(x) = 3(x-2)^2 + 2 , determine the derivative of the function and find the equation of the line tangent to f(x) when x is 4. b) The points of intersection between the lines tangent to g(x) when x=2 and the line tangent to f(x) when x=5 are the centers of three circles with a radius of 5. Determine the equations of the circles where g(x)= squareroot[x] .