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For the given function, simultaneously graph the functions
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Calculus & Its Applications (14th Edition)
- 1) Describe the purpose of finding the first and second derivatives to sketch a graph of functions. 2) Find all relative extrema using the second derivative test.a. f(x) = x^2(6 − x)^3b. g(x) = x^3 −5x^2 +7xarrow_forwardApplying implicit differentiation, find the derivative of the function 1/x + 1/y = 1arrow_forward1)Describe the purpose of finding the first and second derivatives to sketch a graph of functions. 2)Find all relative extrema using the second derivative test. a. f(x) = x^2(6 − x)^3b. g(x) = x^3 −5x2 +7xarrow_forward
- Topic is numerical differentiation Evaluate the derivative if a = 68, b = 0.4, and c = 5 at x = 2 using FDA with Δx =0.02. Round off the final answer to five decimal places.arrow_forwardExample: Let f(x)=x^2-1/x^2+1 The first derivative is shown in the image below.arrow_forward■ Find y 2 implicit differentiation. x3 + y3 = 1arrow_forward
- Graph of f(x) is provided in the image. Sketch the graph of the derivative function f'(x).arrow_forwardImplicit differentiation Use implicit differentiation to finddy/dx. y = xeyarrow_forwardFind 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) = √x, (x0, y0) = (−4, 0)arrow_forward
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