function that is differentiable for all real numbers, and let f(r) 3e +e+5g(x)+4r2- V Find f'(x) (b) Suppose that a functionh is such that h(-1) = 5 and h'(x) = 2x + 3. Find the equation of the tangent line to the curve y h(r) at the point (-1, 5).
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- Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the equation f′(x) = (y0 − y)/(x0 − x) f(x) = 2/x (x0, y0) = (5, 0)a. Find the function f given that the slope of the tangent line to the graph of f at any point (x,f(x)) is xe-2x and that the graph passes through the point (0,3). b. In keeping with the projected increase in worldwide demand for steam coal, the boilerfiring fuel used for generating electricity, the management of Consolidated Mining has decided to step up its mining operations. Plans call for increasing the yearly production of steam coal over its current level by: 2te-0.05t million metric tons/year for the next 20 years. The current yearly production is 20 million metric tons. Find a function that describes Consolidated’s total production of steam coal at the end of t years. How much coal will Consolidated have produced over the next 20 years if this plan is carried out?A. Note on Jacobian dterminants and also give economic interpretation of total differentiation. Also discuss the importance of derivatives. Find the derivatives of the following: A) Y = (2x2 + 16) (6x + 10) B) Y = (14x2 + 12) ( 3x-1 - 9)
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