DIRECTION: Show the complete solution in solving the critical values and the points of inflection of the given function. Explain also the concavity of the points and determine the extreme points of the given function by using a. FIRST DERIVATIVE TEST (FDT) b. SECOND DERIVATIVE TEST Show the complete solution using the two tests. Then, graph the function. Given function: y = x(x + 3)²

Q: Use the four-step process to find the slope of the tangent line to the graph of the given function…

A: The given function is  fx=2x2+7x. step 1:  fx+h=2x+h2+7x+h=2x2+2xh+h2+7x+h=2x2+4xh+2h2+7x+7h Step 2:…

Q: 4. y = x? 3

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A:

Q: Use the four-step process to find the slope of the tangent line to the graph of the given function…

A:

Q: Find the points of discontinuity for the function, f (x) = V6x + 3. Identify the type of…

A: Given function is f(x)=√(6x+3)

Q: 11. Please explain how to get the domain, y-intercepts, zeros of the function, the x-intercepts,…

A:

Q: Q3) A) Graph the two equations and find the points in which graphs intersect x+y = 0, y= -(x- 1) TA…

A: A) The graph is shown below:

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A: Given - A function To Find - Interval where f(x) is differentiable

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ –…

A:

Q: Determine all maximum and minimum turning points of the function: y= 3x* + &r' -90 Find also, the…

A:

Q: Solve this problem algebraically, using your knowledge of derivatives. Do not solve by graphing.…

A:

Q: Find the maximum and minimum values of the given functions using the Second Derivative Test and…

A: Given y=x2-25   ..... (1) The first derivative of the given equation is, dydx=2x Now, dydx=0⇒x=0

Q: How do I solve this question? The altitude of a right triangle is 18 cm. Let h be the length of the…

A: Let a and b be length of altitude and base of triangle respectively. It is given that length of…

Q: Evaluate f sec x dx. Show your solution. Upload Choose a File

A:

Q: Graph the function. Then use the derivative and algebra to find the location of the critical points…

A: We will use a graphing calculator to graph the function.

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A:

Q: Find the point on the line y = x that is closest to the point (5, 7). [Hint: Express the distance d…

A: NOTE: Refresh your page if you can't see any equations. . the given line is  so any point on the…

Q: Complete detailed solution. What is the derivative of 3 f(x)=4x² + -5 √√x

A:

Q: Using the first and second derivatives, predict then sketch the behavior of the functions below,…

A:

Q: Complete detailed solution. What is the derivative of f(x)= 1 (2²-²-x) (-1+√x²) X x+1

A:

Q: Is there a function whose graph doesn’t have a tangent at some point? Explain by giving an example…

A: We have to show whether their exists a function whose graph doesn’t have a tangent at some point.

Q: Tina was observing the changing heights of a ball as it bounced over time. She graphed the function…

A: We need to explain the nature of the graph drawn .

Q: An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is…

A:

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A:

Q: Over what intervals of the domain is the function positive? Negative?

A: From the given graph, it is observed that the domain of the graph is -∞,∞.

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

A:

Q: Using the 2nd Derivative Test, find all relative extrema of f (x) = 2x - 3x-4. Justify your answers.

A:

Q: Find the maximum and minimum values of the given functions using the Second Derivative Test and…

A: For the critical points find the first derivative and equate it to zero. Points of inflexion and…

Q: Find an equation of the line tangent to the graph of f(x) = (5x-9)(x + 6) at (2,8). The equation of…

A: F(x) = (5x -9)(x+6)  at point (2,8) here we have to find tangent equation  so tangent slope = slope…

Q: The function y(x) satisfies the equation 25x2-10y+1/2y2. What is the value of the second derivative…

A: It is given that yx satisfies 25x2-10y+y22=0. Differentiate 25x2-10y+y22=0 with respect to x as…

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A: Given function is  y=x2x2−16

Q: Use the four-step process to find the slope of the tangent line to the graph of the given function…

A: Topic = Functions

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A:

Q: State the domain and range of the function. (Enter your answers using interval notation.) y = Vx + 4…

A:

Q: A function is given below.  What is the slope of the curve, y, at the point (-3, -11)?…

A:

Q: Determine the set of points (x, y) ∈ R2 where we have y as a function of x according to the equation…

A:

Q: Find the x-coordinates of all local maxima using the second derivative test. h(x) = a® – 4x5 + 10 If…

A: To find the x-coordinates of all local maxima of hx=x6-4x5+10

Q: Find the slope of the function at the given point. 3 (6x - 3x + 4)° at the point (1, 343) Type your…

A: We have to find slope

Q: Determine the yange of the function what is the range of y=3 secx? write answer in interval…

A: Consider the given function, y = 3sec(x). Find range graphically: The range of the function is set…

Q: Find the x-coordinates of all local maxima using the second derivative test. h(x) = x° – 4x + 10 If…

A:

Q: Find the equation of the tangent line to the graph of the function f(x)=(x^2+9)(x-3) at the point…

A: Given : f(x) =(x2+9) (x-3)

Q: Find the equation of the line tangent to the graph of the given function at the point with the…

A:

Q: Using at least 3 points, graph the function f(x) =/

A:

Q: Need help with entirety of the problem. Greatly appreciate all the help!

A: Here more than three subparts. So, we will do here starting three subparts. Please resubmit your…

Q: Shantel and her friends are driving across the US from New York to Los Angeles at a constan speed…

A:

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A:

Q: Choose the graph of a function having the given properties. From x 0 to x10 the function increases…

A:

Q: An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is…

A: Solution is given below...

Q: Identify the point of diminishing returns for the input-output function. R is the revenue and x is…

A: Given the Revenue function R=-4/7(x3-3x-5). We need to find the point of diminishing returns for…