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- What is the purpose of the Intermediate Value Theorem?Estimate the slope of the tangent line to f(x) = tax(x) at the point x = 9π/4A particle moves on the line y = 2x + 1 in such a way that its x−coordinate changes at a constant rate of 4 units per second. A right triangle is formed by the vertical line from the particle to the x−axis, the line connecting the particle to the origin, and the x−axis. At what rate is the area of the right triangle changing when x = 4?
- A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x − x2 ), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 2.State the limit of the derivative f’(x) = square root of x+3, f’(2)What are the values of x where tangent line of graph of f(x)=1/x is parallel to the line y=−5x+4.Give exact answers (not decimal approximations).
- If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f (x) = 1 / y (x), what is the average rate of change of the function f ( x) In the same period ?!A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact dimensions (do NOT round) of the triangle be in order to maximize its area? Use the First and Second Derivative TestsWhere are the functions in differentiable???