1.) f(x)= Relative Find all critical numbers and use the First Derivative Test to classify each as the location of a relative maximum, relative minimum or neither. You may use a chart or a number line to perform your sign tests. unction 2.) f(x)=√√x² + 3x²mber of the Binction X 1+x³ la
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- Find the coordinates of all critical points of the given function. Determine whethereach critical point is a relative maximum, a relative minimum, or neither, by first applying thesecond derivative test, and, if the test fails, by some other method. f(x) = 3x^3 − 9x + 3Find the x coordinates of all critical points of the given function. Determine whether each critical point is relative maximum, a relative minimum, or neither, by first applying the second derivative test, and, if the test fails, by some other method. g(x)=2x^3-6x+7 x=____(smaller value) x=____(larger value) Consider the function ƒ(x) = x3. Where is the critical pointof ƒ? Does ƒ have a local maximum or minimum at the critical point?
- Graph afunction on the interval [−2, 5] having the givencharacteristics.Relative minimum at x = −1Critical number (but no extremum) at x = 0Absolute maximum at x = 2Absolute minimum at x = 5Find the critical points and the intervals on which the function y = x4 + x3 is increasing or decreasing. Use the First Derivative Test to determine whether the critical point yields a local min or max ( or neither).Determine whether the following statement is true or false, and explain why. The cosine function has an infinite number of critical points where an absolute minimum occurs.
- 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)2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?Find any critical numbers for ƒ and then use the second derivative test to decide whether the critical numbers lead to relative maxima or relative minima. If ƒ″ (c) = 0 or ƒ″ (c) does not exist for a critical number c, then the second derivative test gives no information. In this case, use the first derivative test instead ƒ(x) = x3
- A rectangular fence is to be constructed with one of its face adjacent to an existing wall. Given that the available materials for the fence are good for 24m, what dimensions will produce a maximum area for the fence? What is/are the function's critical point/sUse the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local maximum, local minimum, or neither.construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. 2.dxdt=−x3+2y3,dydt=−2xy2; stable (at least)dxdt=−x3+2y3,dydt=−2xy2; stable at least