Use the given derivative to find all critical points of f, and at each critical point determine whether a relative maximum, relative minimum, or neither occurs. Assume that f is continuous everywhere. 5- 6x f'(x) = 9 + xA
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- 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). ƒ(x) = √x ln x on (0, ∞)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
- Leth(x) = arctan(x2+ 2x). Find all critical values (if any) ofhand use the second derivative test todetermine where all the local extrema of the function are. You should show all your work calculatingthe second derivative.Find the t coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, minimum, or neither by first applying the second derivative test, and if the test fails, by some other method. t=______(smaller value) t=______(larger value)The derivative of ƒ(x) = x2 is zero at x = 0, but ƒ is not a con-stant function. Doesn’t this contradict the corollary of the Mean Value Theorem that says that functions with zero derivatives are constant? Give reasons for your answer.
- a function f(x) has derivative f'(x)=(x+7)^2(x+3)(x-1)^3. Which are true of f(x)? 1. x=-3 is relative min, and there's one other extremum x=-3 is relative max, and there's one other extremum x=-3 is relative minimum, and there's no other extrema x=-3 is relative max, and there's no other extremum x=-3 is max and there are 2 other extremaA function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a local maximum? A local minimum?(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 identify all relative extrema
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