х3 — Зх2 + 5 f (x) = х3 + 1

Q: Find the indicated derivative. 3 If f(x) = 24³x² + 96 3 VX find f'(8).

A: Here we will find f'(8),

Q: Given the function, find the derivative f (x) = -()" 3z 4 3z- 3 12() 3z-4 O None of the Above

A:

Q: 3. sol Griven fun CHen. frxidz)= 9x2

A: To determine the first derivative ∇f of the given function.fx, y, z=2x3y2z2

Q: For the function y = (9x2 - 27)/x3 , determine the increasing and decreasing intervals, and identify…

A:

Q: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) = 2x - 6/7

A: Explanation: Given that,  f(x)=2x-67

Q: Find an equation for the line tangent to f(x)=x3 +3x2 -2x-8, at the point where x=1

A: To find the equation of the tangent line at point x = 1 for the given curve.

Q: Find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Given a function 'f' of x and find its first derivative . And also find at x=1 tengent line equation…

Q: Given the functionf(x)=(x-1)', find the slope of the line tangent to the graph of fat the point…

A: Given :

Q: For the​ function, find the points on the graph at which the tangent line is horizontal. If none​…

A:

Q: On the graph of f(x)=sinx and the interval [2π,4π), for what value of x does the graph cross the…

A: The given function is fx=sinx. Calculate the interval [2π,4π), for what value of x does the graph…

Q: If x + y represents a motorboat’s average velocity with the current, in miles per hour, its distance…

A: We can say Average Velocity=Average DisplacementTotal time=dt so according to the question…

Q: Find the derivative of the function f(x) (3x+6)? 6x2+13

A:

Q: Given the function f(x) =4x³– 39x²+90x +2, which of the following describes its absolute extrema at…

A: Given that, The function is following, f(x) = 4x3 - 39x2 + 90x + 2 We have to find the absolute…

Q: Jx + 2x f(x)=- 7х — 4х? 8.

A:

Q: Find the derivative of the function. q=5√x³+3x q' =

A:

Q: Q2: By the false position method, find approximation value of the root for f(x) = ex - 2 with &…

A: False Position Method : An algorithm for finding roots which retains that prior estimate for which…

Q: Find the value(s) of a for wh has range of all real numbers.

A:

Q: Find an equation for the functionf that has the given derivative and whose graph passes through the…

A:

Q: for the function f(x)=11x^3-x, find the slope of secant line at interval [1, 1.01]

A: We have given a function f(x).

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = 2° – 3x7 +2

A:

Q: 2. Given f(x) = x³ – 7x? + 16x - 10 find the location of all horizontal tangent lines.

A:

Q: If f(5) 3 andf'(5)=-2 , find the derivative of x²f(x) at x 5. А. В. -18 С. -12 D. -20 Е. -80

A: we have to derivative

Q: Find the values of ôf / ôx at the point (4,-5) if f(x, y) = x +3xy + y-1

A:

Q: 5. Iny+ea²²x+y = 10 -

A: The given equation is lny+ex2y2-x+y=10. Find the derivative of the equation. Here we use the…

Q: Determine the interval(s) for which f(x) = x4 – 54x² is concave down. Answer:

A:

Q: Find the derivative (3t - 4) ^8 divided by t + 9

A:

Q: If f(y) = V4 - 7y, find f'(y). Use exact values.

A:

Q: The graph of f(x)=2x^3+6x^2−144x+6 has two horizontal tangents. what are the positive and negative…

A: See the details solution in below

Q: -4 y = x2iy(3)

A:

Q: Ex 5. Find the intervals of increase or decrease for f(x) = (x– 2) Vx² .

A: We have to find the interval where derivative of f is positive and negative

Q: Find the derivative of the functionf(x)= 9x² + 4x +6, using the definition of the derivative,

A:

Q: Find the point(s) at which the slope of the tangent line is equal to 21. And find the equation of…

A: First we differenciate given function and put equal to slope 21 from there we get value of x and…

Q: a) Find and locate local extreme values off(x) = (x+ 1)^4−4x−2, (b) Then find the intervals of…

A: Given,            f(x) = (x+1)4 − 4x − 2

Q: If a ball is thrown into the air with a velocity of 40 ft/s, its height (in feet) after t seconds is…

A:

Q: For f(x) = (4x – 2)°, find the equation of the tangent line at x = and x = 2. The tangent line at x…

A:

Q: -y = a(10z² –8z+7)

A: Using composite derivative formula.

Q: For the function f(x)= 3x² +2x–1, Find the equation of the line tangent to the curve at x = -1 2.

A:

Q: Q2: By the false position method, find approximation value of the root for f (x) = ex – 2 with e…

A: Consider the given function. fx=ex-2 The false position method is defined as,…

Q: Find the derivative of the function. q= 5 3 x + 6x

A: The given function q=x3+6x5

Q: Using the function f(x) = − 4x² + 6x + 1, find the slope over the interval listed below: - [-9,5] m=

A: Please refer to the image below

Q: given y=f(x) and the function is linear, use this change equation to solve the problem. Given that…

A: We have to use the given differential equation.

Q: Find all the values of x where the graph of f(x) = 2x³-36x2 + 192x 9 has a horizontal tangent line.…

A: topic - derivative of a function and point of horizontal tangent line

Q: Find derivative the He' 3x+2

A:

Q: f(x) = avbx – c - the x -axis and the line x = 17 using Trapezoidal Rule with 6 equal intervals if a…

A:

Q: f (x) = 5x³ – 3x? + 10x – 5 , find the fourth derivative f(4)(x) If - Select one: о а. 30х b. 0 С. Х…

A:

Q: 4. Given the function y = 2x³ - 4x² + 5, find its derivative.

A: Differentiate with respect to x

Q: On the graph of f(x) = sin x and the interval 0, 27), for what value of x does the graph cross the…

A: f(x) = sinx Any Function crosses the x- axis when its y- value becomes 0

Q: For the function f(x) 5x³ – 8x² + 8, , Step 1 of 2: Find the slope of the tangent line at x = 1.

A:

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.