Let f(x) = x^3. Find a value "C" between x=0 and x=12 such that the average...

Let f(x) = x^3.

Find a value "C" between x=0 and x=12 such that the average rate of change of f(x) from x=0 to x=12 is equal to the instantaneous rate of change of f(x) at x=C

Expert Solution

milcah answered 2 years ago

Let f(x)=−(3x^3+8) (a) List the critical point(s) of f= (b) f′(x)>0f′(x)>0 for x∈= (c) f′(x)<0f′(x)<0 for...

Let f(x)=−(3x^3+8) (a) List the critical point(s) of f= (b) f′(x)>0f′(x)>0 for x∈= (c) f′(x)<0f′(x)<0 for x∈= Note: the answers to the above questions can be a value, a list of values, an interval, a union of intervals, or "NONE" if no values exist.

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a...

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a so that f(x) is a probability density function b)What is P(X<=1)

Let f(x)=3x^3−7 A) List the critical point(s) of f= B)f′(x)>0f′(x)>0 for x∈= C)f′(x)<0f′(x)<0 for x∈= D)The...

Let f(x)=3x^3−7 A) List the critical point(s) of f= B)f′(x)>0f′(x)>0 for x∈= C)f′(x)<0f′(x)<0 for x∈= D)The local maxima of ff occur at x= E)=The local minima of ff occur at x= nstructions: For part (1), give your answer as a single value, or a list of values, or the word none . For parts (2) and (3), give your answer as an interval or a union of intervals, such as (0,1) or (-inf, 2) U (3,4), or the word none....

Let ?(?)=12?2f(x)=12x2. (a) If we wish to find the point ?=(?0,?0)Q=(x0,y0) on the graph of ?(?)f(x)...

Let ?(?)=12?2f(x)=12x2. (a) If we wish to find the point ?=(?0,?0)Q=(x0,y0) on the graph of ?(?)f(x) that is closest to the point ?=(4,1)P=(4,1), what is the objective function? (Hint: optimize the square of the distance from ?P to ?Q.) Objective function: ?(?)=O(x)=____________________________ (b) Find the point ?=(?0,?0)Q=(x0,y0) as described in part (a). Box your final answer. (c) Verify that the line connecting ?P to ?Q is perpendicular to the line tangent to ?(?)f(x) at ?Q. Hint: recall that the lines ?=?1?+?1y=m1x+b1...

If f(x) = exg(x), where g(0) = 3 and g'(0) = 4, find f '(0).

If \(f(x)=e^{x} g(x),\) where \(g(0)=3\) and \(g(0)=4,\) find \(f(0)\)

9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11,...

9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11, 11) for which the line tangent to the graph of f is parallel to the line joining (−11, f (−11)) and (11, f(11)). How many such numbers exist in the given interval? . 0 . 1 . 2 (correct) . 3 Enter points in increasing order (smallest first). Enter DNE in any empty answer blank. c = c = c = DNE (correct) 10....

1. Find the average value of the function f(x)= 1/ (x^2-9) on the interval from 0...

1. Find the average value of the function f(x)= 1/ (x^2-9) on the interval from 0 ≤ x ≤ 1 2. Find the arc-length of the function f(x)= x^2 from 0 ≤ x ≤ 2

Find f. f ''(x) = x−2, x > 0, f(1) = 0, f(4) = 0 f(x)=

Let F(x) = log5x and H(x) = x . Find the value of F(H(25)). Write the...

Let F(x) = log5x and H(x) = x . Find the value of F(H(25)). Write the equation of a circle whose center is located at (-2, -5) with a radius of 11 inches. Given a triangle with Angle A = 45 degrees, Angle B = 60 degrees and side a = 10 inches. Find the length of side b. (Leave answer in radical form.) Find the distance between a set of points whose coordinates are A(-7, 8) and B(5, -11)....

Find f. f ''(x) = 4 + 6x + 24x2, f(0) = 4, f (1) = 12

Question