Is the graph of g(x)=4x^3+9x^2+7x+3 concave up or down at the point with x-coordinate −2?

Q: What is the slope of the line tangent to the graph of a function defined by f(x)= 2x²-4x+5 at…

A: f(x)=2x2-4x+5Let y=2x2-4x+5Differentiate

Q: Find the equation of the line tangent to the graph of y = 2x - 8x2 + 2x -6 at x = 2. | %3D

A:

Q: Find the equation of the tangent line to the graph of x4 y2 = 144 at the point (2, 3) and at the…

A: Equation of the tangent line to the graph of x4y2=144 at the point (2, 3) Now, differentiate the…

Q: Find an eqaution of the line tangent to the graph f(x) = 3x2 - 5x at the point (1,-2).

A: fx=3x2-5x Slope of the tangent line is the derivative of the given function at the given point. So…

Q: What is the maximum slope of a tangent to the function f(x) -x³ + 4x - 2? ==

A:

Q: sketch the shifted exponential curves y = 3x + 2 and y = 3-x + 2

A:

Q: .Suppose that a company produced and sold two types of products. If they sold monthly x, items of…

A: To determine the income if a company sold 32000 items of the first product and 55000 items of the…

Q: The slope of the tangent line to the graph of the function y = 2x3 at the point (2, 16) is lim2"…

A:

Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: What is the slope of the tangent line to the graph of the solution of y' = 5√y + 3x³ that passes…

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Suppose 275 trout are seeded into a lake. Absent constraint, their population will grow by 75% a…

A: Given problem Given that   Suppose 275 trout are seeded into a lake. Absent constraint, their…

Q: Find the slope and y-intercept of the line through the point (1,5) that cuts off the least area from…

A: In the question we have to find slope of line and y-intercept.

Q: Use the derivative to find the vertex of parabola. y = -2x2 + 12x - 5

A: Given equation of parabola is y=-2x2+12x-5. To find the vertex using derivative. Solution: We know…

Q: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

Q: .ב -ב

A: Topic:- Functions  Your answer is incorrect.  see the correct answer below

Q: What is the slope of the tangent line to the graph of the solution of y' = 7√x + 6x³ that passes…

A:

Q: Explain how to write an equation of the tangent line to the graph of f(x) = x2 at (2, 4).

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

A:

Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

A:

Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

A:

Q: Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 35% a…

A:

Q: Find the equation of the line tangent to the graph of f(x) = 4x° + 6x2 – 6x – 5 at x = -6. %3D

A: The function is given by fx = 4x3+6x2-6x-5 To evaluate: The equation of the tangent line to the…

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A:

Q: 1 What is the family of the equation y %3D quadratic exponential linear

A:

Q: Suppose 225 trout are seeded into a lake. Absent constraint, their population will grow by 60% a…

A: Since the growth rate is given in terms of percentage for first of all we will convert into decimal…

Q: Write the equation of the tangent line to the graph of  y = (8x2 − 6x + 2)(1 + 2x) at x = 1. Check…

A: the equation of the tangent line to the graph of, y=(8x2−6x+2)(1+2x) at x=1   y=(812−61+2)(1+21)…

Q: at the line x = 3. %3D

A: Find the volume of the solid generated by revolving the region between the parabola  x=y2+1 and the…

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

A:

Q: Suppose 175 trout are seeded into a lake. Absent constraint, their population will grow by 60% a…

A: Recall: Logistic growth model   P(t)=m1+m-PPe-ktWe have, P=175, m=2000, k=60%=0.60, t=5 years

Q: Locate root of the equation x +x- 2 = 0 using fixed point method.

A:

Q: Find the equation of a tangent line to the graph of f(x) = x² – 2X at (-2,8). TYPE IN THE EQUATION…

A:

Q: There is a line through the origin that divides the region bounded by the parabola v X-axis into two…

A: Given- There is a line through the origin that divides the region bounded by the parabola y = 7x -…

Q: An fruit grower knows from previous experience and careful data analysis that if the fruit on a…

A: The average pounds of fruits is 130 pounds, and the selling price is $0.6 per pound. The yield per…

Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A: We have to find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis…

Q: Suppose 275 trout are seeded into a lake. Absent constraint, their population will grow by 50% a…

A:

Q: Write the equation of the tangent line to the graph ofy = (7x2 − 6x + 2)(1 + 2x)atx = 1.

A: we have to find tangent line to f(x) at x=1first we will compute tangent point at x=1

Q: find tangent line to the curve y=3x/7-x at a point of (-3,2/7)

A:

Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

A:

Q: Find the equation of the line tangent to the graph f(x)= (lnx)5 at x=5

A: First find slope then use equation of tangent tangent line

Q: An fruit grower knows from previous experience and careful data analysis that if the fruit on a…

A: To find: How many weeks should the grower wait to maximise the sales revenue per tree.  Find the…

Q: Help 18 cubic function whose graph has horizontal tangents at (-2,6) and (2₁0). {Y= ax ³ + bx²²…

A: Let's solve.

Q: Find the slope and y-intercept of the line through the point (2,7) that cuts off the least area from…

A:

Q: find the slope of the line tangent tothe graph of ƒ(x) = -5x + 1 at the point (1, -4).

A: We have to find slope of tangent line to the graph of fx=-5x+1 at the point 1, -4. We know that…

Q: Graph the given parabola by determining the vertices and using first derivative test y = 3x4- 8x +…

A: Given parabola:                              y=3x4-8x3+6x2            Let's find the y-intercept for…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.