Let f(x) = 8x10 – 5æ°. %3! - (a) Use the definition of a derivative or the derivative rules to find f' (x) (b) Use the definition of a derivative or the derivative rules to find f"(x) (c) On what open interval is f increasing? 8, 16
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- find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the domains of the function and its derivative. must show all stepsFind the local maximum and minimum values of f(x) = x^5 -5x +3 using the second derivative test when it is not possible use the first derivative testfind the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the domains of the function and its derivative
- with the limit definition of a derivative find the derivative of g(x) = (x-1)^2 + 1find the derivative of g(x) = (x+5)/(5-2X) using the definition of the derivative. must show all steps.State the limit definition of the derivative for a function g(x) at any point x, and use it to find the derivative for the function g(x)=1/5-3x
- Use the definition of the derviative to compute the derivative of f(x)=1−3x2f(x)=1−3x2 at the specific point x=2x=2. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).For the function f(x) = x^2/x+1, 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.Use the definition of a derivative to find the derivative of f(x)=x^2+5x-8 show all steps with limit notation
- Find the critical numbers of f, if any, (a) find the open intervals on which the function is increasing or decreasing, (b) apply the First Derivative Test to identify all relative extrema, and (c) use a graphing utility to confirm your results. f(x) = x2 + 6x + 10Let f(x)=4x 2+12x−2Using the definition of derivative, f'(x)=limh→0 f(x+h)−f(x) /h,enter the expression needed to find the derivative at x=3.f'(x)=limh→0 After evaluating this limit, we see that f'(x)= Finally, the equation of the tangent line to f(x), in point-slope form, where x=3 is ------Find the local maximum and minimum values of the function f(x)=-x-(25/x). using the Second Derivative Test.