Question

In: Math

Consider the graph defined by f(x) = (x-3)2 a) state the coordinates of the vertex and...

Consider the graph defined by f(x) = (x-3)2

a) state the coordinates of the vertex and the direction of opening of f(x)

b) Find the maximum and minimum values of f(x) on the interval 3<=x<=6

c) Explain how you could find part b) without finding the derivative

Solutions

Expert Solution

if you have any doubt please comment/please like


Related Solutions

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)...
Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = x2 + 8x - 8
Consider the function f(x)= 7 - 7x^2/3 defined on the interval [-1, 1]. State which of...
Consider the function f(x)= 7 - 7x^2/3 defined on the interval [-1, 1]. State which of the three hypotheses of Rolle’s Theorem fail(s) for f(x) on the given interval.
1. Consider the following curve f(x)= X^3 - 5x^2 +7x-5 Find the coordinates of the minimum and the maximum.
  1. Consider the following curve f(x)= X^3 - 5x^2 +7x-5 Find the coordinates of the minimum and the maximum. 2. The curve y= x^3 + ax^2 + bx + c has a relative max at x=-3 and a relative minimum at x= 1. Find the values of a and b. 3. Find the equation of the perpendicular line to the curve x^2 + 2xy - 2y^2 + x=2 at the point (-4,1) 4. Find the slant asymptote f(x)= (4x^2...
Consider f(x) = 2 + 3x^2 − x^3
Consider f(x) = 2 + 3x2 − x3 a) Find local max and min values b) Find intervals of concavity and infection points
Let f(x)=(x^2+1)*(2x-3) Find the equation of the line tangent to the graph of f(x) at x=3....
Let f(x)=(x^2+1)*(2x-3) Find the equation of the line tangent to the graph of f(x) at x=3. Find the value(s) of x where the tangent line is horizontal.
Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...
Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals where f is positive and where f is negative. Does f have any horizontal or vertical asymptotes. If so, find them, and show your supporting calculations. If not, briefly explain why not. Compute f′ and use it to determine the intervals where f is increasing and the intervals where f is decreasing. Find the coordinates of the local extrema of f Make a rough...
Graph the function f(x) = 3.5(2)x. State the domain and range and give the y-intercept.
Graph the function f(x) = 3.5(2)x. State the domain and range and give the y-intercept.
Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2....
Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2. (a) Randomly pick a sample of size 20 from this distribution, find the probability that there are 2 to 4 (inclusive) of these taking negative values. (b) Randomly pick an observation X from this distribution, find the probability that it is between 1.2 and 1.4, i.e., P (1.2 < X < 1.4). (c) Randomly pick a sample of size 40 from this distribution, and...
5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of...
5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of the function and all its x and y intercepts. (b) Is the function even or odd or neither? (c) Find the critical points, all local extreme values of f, and the intervals on which f is increasing or decreasing. (d) Find the intervals where f is concave up or concave down and all inflection points. (e) Use the information you have found to sketch...
Consider the following functions. f(x) = x − 3, g(x) = |x + 3| Find (f...
Consider the following functions. f(x) = x − 3, g(x) = |x + 3| Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT