Evaluate the function f(x) at the given numbers (correct to six decimal places) Зе^ - 3- Зх x x2 1, 0.5, 0.1, 0.05, 0.01, -1, -0.5, -0.1, -0.05, -0.01 f(x) f(-1)-1.103638 X f(-0.5)-1.278368 X f(-0.1)-1.451225 X f(-0.05)1.475309 f(-0.01)-1.495012

Q: Plot the function using a graphing utility and find its critical points and extreme values on [−5,…

A:

Q: The dose-response curve for x grams of a drug is f(x) = 8(x – 1)3 + 8 for (x 2 0). (a) Make a sign…

A: We have to find the signs for the first derivatives and second derivative for the function  f(x) =…

Q: Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics…

A: Given query is to find the time when concentration is maximum and rate of change nis increasing.

Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

A: average rate of change= -7 for detail...go through the solution

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: We have to find average rate of change of the function f(x)=6xr+y on [x, x+h]

Q: Determine the intervals where the function f(x)= lnx/x is increasing and where it is decreasing.

A:

Q: Find the derivative by the limit process. f(x) = 15 – x2 Step 1 Complete the definition of a…

A:

Q: Verify Mean Value Theorem for the function f(x) = in interval [0,9]

A: If a function  f(x) is continuous at the range [a, b] and also differentiable in the range (a, b)…

Q: Make a table of values for the function F(x) = (x + 2)/(x - 2)at the points x = 1.2, x = 11/10, x =…

A: F(x) = (x + 2)/(x - 2) List of points  x = 1.2, x = 11/10, x = 101/100, x = 1001/1000,x =…

Q: Verify Mean value theorem for the function f(x)=2x^3+x+3 over the interval [0,1

A: Topic-Calculas

Q: draw a graph to match the description given.  f(x) has a negative derivative over (-infinity, 2) and…

A:

Q: Determine the absolute error and relative error when approximating the derivative of f(x) = -x² + 5x…

A:

Q: Determine where the given function is increasing and where it is decreasing. f(x) = x2(4 - x)2…

A: Solve by first derivative test

Q: Find a function

A: This is very intresting question because there are so many function on an interval whose first…

Q: 1. Differentiate a trig function that is greater than a power of 1, and involve either quotient,…

A:

Q: The function f(x) = vx – 2 + V4 – x is – increasing on (-∞, 3) and decreasing on (3, 0) decreasing…

A:

Q: ) Calculate the derivative of f1 (x) = 2x4 - 3x3 + 1/2x2 + 3. b) Study the sign of the derivative…

A:

Q: Sketch a graph of the following function by the guidelines: y = 4x3 – 6x? – - a. The behavior of y…

A:

Q: Find the critical point and determine if the function is increasing or decreasing on the given…

A:

Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3rVx+ 2 10 4. -…

A:

Q: Find the average rate of change of the function f(x) = x² - 2x + 3 between x = -2 and 2 = 4. Type an…

A:

Q: Suppose that the second derivative of a function f is f"(x)= -(x+1) (x – 1)²(x - 4)°. Determine the…

A: To find the inflection point and intervals of concavity

Q: 4. Using the first derivative test to find the location of the local maxima of the following…

A: Given function :

Q: For the drug metabolism function f(x) = -x(x+2)(x-3) , find the average rate of change of f(x) on…

A:

Q: The first derivative of the function h is given by h' (x) = 15 - 3z² +z. What are all intervals on…

A: solution:-h'(x)=x5-3x2+x2nd derivative…

Q: Use the first and second derivative to graph the following function. Label all critical points,…

A: Given that: y=4x3-4x2-8x

Q: The second derivative has already been found and factored to be f"(x) = (5x)(x+2). Use interval…

A:

Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3xVx + 2 10 -2 4…

A: The given function is fx=-3xx+2.

Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3xVx + 2 10 -2…

A:

Q: Calculate the approximation M4 for the given function and interval. f(x) = 5-*, [1,3] (Use decimal…

A: Given that f(x) = 5-x, [1, 3]

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: The average rate of function f(x) on the interval a,b is given by  average rate of change = fb-fab-a…

Q: Order from narrowest to widest: f(x) =x² g(x) = -3x² +1 h(x) =0.5x -2 k(x) = 0.01x² + 100 k(x) ,…

A: Compare the given functions to an standard form of quadratic polynomial.

Q: Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable.…

A: The objective is to find relative extrema, if any, of the function.

Q: Find the average rate of change of the function from x1 to x2. Function x-Values f(x) = −3x +…

A: Function      x-Values f(x) = −3x + 19      x1 = 0, x2 = 3

Q: Find all the relative and absolute extrema of the given function on the largest possible domain.…

A: Given,  g(x)=(x-6)2/3

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: The given function is fx=2x2+5. The average rate of change of a function f over the interval x,x+h…

Q: Find the derivative by the limit process. f(x)=14-x² Step 1 Complete the definition of a derivative.…

A: topic:- calculus

Q: Find the critical point and determine if the function is increasing or decreasing on the given…

A: given function     y = x5/2 -2x2 ,  x > 0

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A:

Q: Find the critical points and the interval on which the given function is increasing or decreasing…

A: We find F'(x) using the power rule

Q: Sketch a graph of the following function by the guidelines: 1. y = 4x3 – 6x² – 24x 2. y = 2x3 + 3x²…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

A: A critical point is a point where the derivative of the function is 0 or does not exist. At critical…

Q: Suppose the derivative of the function y = f(x) is y = x!/5(x +5). Determine the intervals on which…

A: Given y=fxy'=x15x+5 To find intervals in which f(x) is increasing and decreasing

Q: A function and its graph are given. Use the second derivative to determine each of the following.…

A:

Q: Find the average rate of change of the function from x1 to x2. Function      x-Values f(x) = x2 −…

A:

Q: Draw a graph to match the description given. f(x) has a negative derivative over (-∞,5) and (5,9), a…

A:

Q: Graph the function f(x)=−4x2 and draw the tangent lines to the graph at points whose x-coordinates…

A: Given: fx=-4x2 To Find: a. Draw the tangent line to the graph at points whose x-coordinates are -2,…

Q: Can you please help me step by step with this problem?

A: We can see, that the graph of the function given is a straight line and the slope of the line is…

Q: Let f (x) = (x + 4)²(8 – x). Use the First or Second Derivative Test to find the relative extreme…

A: I use first derivative test to find relative maximum and minimum