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- Draw a graph to match the description given. f(x) has a negative derivative over (−∞,−3) and (3,∞) and a positive derivative over (−3,3), and f′(−3)=0, but f′(3) does not exist.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 −5x2 +7x1) 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 +7x
- Using differentials show how to estimate this (8/ 8.1) ^1/3 in rational numberA 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate of 10 gal/min and the resulting uniform mixture is removed from the tank at the same rate. Derive an expression for the amount of dye in the tank as a function of time. Find the time t at which the tank contains 26% dye solution.Using "Numerical Differentiation (Backward Finite Difference)" Problem Solving f(x) = 2cos (3x-2) with h = 0.002, What is f'(1) and f''(1)?
- Give algebraic proofs that for even and odd functions:(a) even times even = even; odd times odd = even; even times odd = odd;(b) the derivative of an even function is odd; the derivative of an odd function is even.h(x) = 4/((x-1)^2) Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in the interval (-∞, 1) and decreasing in the interval (1,+∞).Give an example of a function f (x) that has one positive derivatives on the range (−1, 0) and a negative derivatives on the range (0, 1).
- using the definition of derivative to find f'(x) for the function:f(x)=4/x. How do I solve this?For the function f(x)= x+1/x . use algebraic methods to determine the interval(s) on which the function is increasing, the interval(s) on which the function is decreasing, and use the First Derivative Test to identify the location (input value), value (output value), and classification (minimum or maximum) of any relative extrema of the function. Give your answers in exact form.2-22 Differentiate the function: f(x) = log10(√x ) ? Please show work along with the rule used for derivatives of logs - Thank you!