The graph of the function f(x) =ax2 +bx +c has its vertex at (0,2) and passes through the point (1,5). Find a,b, and c.

Q: . The graph of the function f(x) = ax2 + bx + c has vertexat 10, 22 and passes through the point 11,…

A: We have  fx=ax2+bx+c To find the vertex of the quadratic equation, differentiate it and equate it to…

Q: The total daily profit (in thousands of pesos) of a certain food company for the sale of x boxes of…

A: Given query is to find the number of box needs to be produced to maximize the profit.

Q: Find the maximum and minimum value of x3+y3-3axy

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Q: The function x2 f(x) = 1 - x has a local maximum when x = 2. Select one:

A: We will check if the given statement is correct.

Q: 21. Find the quadratię function y = ax² + bx + c whose graph passes through the points (-1,0), (1,…

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Q: Find the maximum value of the function f(x) = x² . – x within the interval0 < x < 2. -

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Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

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Q: Find the absolute maximum value of the function f(x) = (x - *).

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Q: Find the formula for a function of the form y=be^((-(x-a)^2)/2) with its maximum at the point (0,5).…

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Q: Find the linearization of the function at a . f(x) = x 4 + 3 x2    , a = -1

A: We know that ,The linearization of the function at v=ais given by fa+f'ax-a

Q: Find the local maximum and minimum points of f (x) = (3x - 1)3.

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Q: Find the critical points of the function f(x)3D7X2-14x.

A: Need to find critical points

Q: Determine critical points of the function f(x)=∣∣x2−4x+3∣∣.

A:

Q: Find the absolute maximum/minimum of function f(x) = x3 - 16x + 1 %3D

A: fx=23x3-16x+1 to find the critical points take derivative=0 ddx23x3-16x+1=0 ddx2x33-ddx16x+ddx1=0…

Q: Find the minimum value of the function. f(x) = -2 - 2x + x2

A:

Q: The graph of function f(x) = x³ 6x2 + 9x + 1 is concave upward on (-∞, 2) (-0, 0) (2, оо) о (-2, 2)

A: f is concave up when f''(x) is greater than 0

Q: Find the point on the graph of the function that is closest to the given point. f(x) = Vx - 6, (15,…

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Q: What is the relative maximum value of f(x) = x³ – 3x + 2? -

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Q: Find the linearization of the function at a . f(x) =  x3/4    , a = 16

A:

Q: Find the maximum and minimum values of the function f(x) = x² – 6.x +7 on the interval [0, 5].

A: It is given that, f(x)=x2-6x+7   , on the interval 0,5We have to find the maximum and minimum values…

Q: The point of the given function at (2, -7) is found to be y = x3 – 2x2 – 4x + 1

A:

Q: For what x does the function f (x) = 1/4 x2 - x + 2, 0 … x … 8, have its maximum value?

A: For a given function f(x) the critical point are the value of x at which the derivative of f(X)…

Q: . Find the local and absolute minima and maxima for the function over (-∞, ∞). 3 y = x³ (1-x)6

A: Given, y=x31-x6

Q: Find the minimum and maximum point of the function f(x)=x3-3x+1

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Q: Find the critical points of the function f(x)=8x3−x4.

A:

Q: 2. Find an equation and sketch the graph of the level curve of the function f (x, y) = 16 – x² - y2…

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Q: Find the point at which the line f(x) = - x – 2 intersects the line g(x) 3x + 6 %3D

A: f(x) = g(x) Thus, -x-2 = 3x + 6   Separate variables to LHS and constants to RHS -x-3x = 6 + 2 -4x =…

Q: Find the point on the graph of the function that is closest to the given point. f(x) = Vx - 4, (15,…

A:

Q: Find a 4th degree function that has solutions X=-4-2/3 and x=-4+2/3, x=2i and x=-2

A: See the attachment

Q: Sketch the graph of the floor function f(x)= |x +1|| over the interval [-3, 3)

A:

Q: Find a function y whose graph passes through the point (1, =) and satisfies x2y' = y.

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find a quadratic function f (x) = ax2 + bx + c which has a vertex at (1, 1) and passes through (3,…

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Q: The graph of a quadratic function f passes through the points (−2, 4), (1, 1) and (5, 0). What is…

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Q: 2) Sketch the graph of the floor function f(x) = x+31 over the interval [-4,2].

A:

Q: Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

A: Given differential equation     x2y'=y   and initial condition  at x=1,y=2/e

Q: Find a formula for the linear function with slope −3 and x-intercept 2.

A: Refer to the question.For the linear function with slope −3 and x-intercept 2, use the slope…

Q: Find the point on the graph of the function f(x) = (x + 5)2 that is closest to the point (1,3). %3D

A:

Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

A:

Q: Please

A: The given function is

Q: Find the maximum and minimum values attained by the function: f(x) = x +-

A: Here the given function as fx=x+5x or fx=x2+5x Differentiate with respect to x…

Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

A: Explanation of the answer is as follows

Q: The graph of function f(x) = x – 9x² + 7x is concave upwards on (-0, c0) O (-∞, 3) O (3, 0) O None

A: Given function is  f(x)= x^3 - 9x^2 + 7x

Q: The graph of f​(z​)=16^z passes through the points (−1,x ), (0,x)and (1,x) simplify

A: The equation of the graph is given that: f(z)=16z. So, when it passes through the points (-1,x), it…

Q: Find the maximum and minimum points of f(x) = x(12 – x)?

A: topic - application of derivatives

Q: Suppose point P (-2, -3) is on some function y=f(x) and is transformed to g(x) so that g(x) = 5f…

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Q: Find the attractive fixed point of g(x) = 4x - x2 4 | 2

A: Fixed point: The point of intersection of y=f(x) and line y=x are known as fixed points: Example:…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.