Using a method show in class, find the intervals on which fis increasing and the intervals on which it is decreasing. f(x) = v2 sin(x) – x on [0, 27]
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- Using the First Derivative Test Consider the function ƒ(x) = 3x4 - 4x3 - 6x2 + 12x + 1.a. Find the intervals on which ƒ is increasing and those on which it is decreasing.b. Identify the local extrema of ƒ.Intervals where f is increasing or decreasing. f(x)=sin(pi(x))-cos(pi(x)) over x=[-1,1]The Second Derivative Test Use the Second Derivative Test to locatethe local extrema of the following functions.a. f(x) = 3x 4 - 4x 3 - 6x 2 + 12x + 1 on [-2, 2] b. f(x) = sin2 x
- Mean Value Theorem. So I determined that this is continuous and differentiable at [1,7]. I just do not know how to find the numbers (c) that satisfy the conclusion of the mean value theorem. f(x)=1/x [1,7]lim x->0 (x)(sinx) divided by (1-cosx) Evaluate the limit. Hint: creating a graph may be helful.Using the definition of monotonicity prove that the function f(x)=cosx is strictly decreasing on the interval [0,π].
- Absolute maxima and minima Determine the location and value of the absolute extreme value of ƒ on the given interval, if they exist. ƒ(x) =sin 3x on [-π/4, π/3]lim xto1 of the function e(2^x) /(x^2) .. use L'Hoptial's Rule1) Find the area (in square units) of the region under the graph of the function f on the interval [−11, 9],using the Fundamental Theorem of Calculus. Then verify your result using geometry. f(x) = 9 2) Find the area (in square units) of the region under the graph of the function f on the interval [−1, 5]. f(x) = 2x + 4
- Where is the function continuous? Differentiable? Use thegraph of ƒ in the figure to do the following.a. Find the values of x in (0, 3) at which ƒ is not continuous.b. Find the values of x in (0, 3) at which ƒ is not differentiable.c. Sketch a graph of ƒ′Local max /min of x1/x Use analytical methods to find all localextrema of the function ƒ(x) = x1/x, for x > 0. Verify your workusing a graphing utility.Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use. f(x)=5sin(2πx),[−1,1]