5) Consider function f (x) = 2x – 1 +5 x+2 %3D a) Compute f'(x) and f"(x) b) Find coordinates of all relative extreme points of f(x) if any c) Find coordinates of all inflection points of f(x) if any d) Consider other properties of the function and draw a neat graph of it. Label importan points on the graph
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- a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimumvalues.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = x - 2 tan-1 x on [-√3, √3]Consider a differentiable function f with domain R and derivativesf'(x)=-aebx(1+bx) and f"(x)=-abebx(2+bx) , with a and b nonzero real numbers.The function has only one critical point x=-1/b and a local maximum at x=-1/bUse the Second Derivative test to find the value(s) of a and b(a) Find the critical numbers of f , if any (b) find the open intervals on which the function is increasing or decreasing, (c) apply the First Derivative Test to indentify all relative extrema and (d) use a graphing ulitulty to confirm your results. f(x)=x2-3x-4/x-2
- Deduction of the second derivative criterion for optimization of functions <br> of two variables using and as related to TaylorFind all the critical points and horizontal and vertical asymptotes of the function f(x)=(x^2+5)/(x-2). Use the First and/or Second Derivative Test to determine whether each critical point is a local maximum, a local minimum, or neither. You may use either test, or both, but you must show your use of the test(s). You do not need to identify any global extrema.Find the area in square units of the region under the graph of the function f on the interval[-10,5] using the fundamental theorem of calculus then verify the result using geometry f(x) = 5
- Let f(x)=cosx. Determine the x-value(s) where the function has a maximum or minimum value on [0,2π). What is x-value(s) occur(s) on [0,2π), the minimum value(s) of the function?Consider the cubic polynomial f (x) = x^3 - x. Find the equation of the tangent line of f(x) at the point (1, 0). Plot both f(x) and the tangent line on the same set of axes (label both). On a new set of axes, plot both f (x) and f "(x) (label both graphs). What do you notice about f(x) and f'(x)?Find all local maximum and minimum for f(x) = 2x3 + 3x2 -12x using the first derivative test. Show me your table.
- set up integrate along y-axis. bound by f(x)=x4 and g(x)= 16x-4x2. Draw approprate differental element on graph and lable all dimensions and features.a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist).