The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) = and f(1) = is the ---Select---v value of f.

Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2

A:

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: Find the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum…

A: Given that: y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection…

Q: Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local…

A:

Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y x³ on the interval 0 0 and p and q are…

A: step:- 1 Generalization using nature of graph In interval (0,1) First draw graphs of x13,x12,x,x2,x3…

Q: Find the quadratic approximation to f(x) = /x + 3 near a = 1. Graph f, the quadratic approximation,…

A: fx=x+3

Q: Apply a sequential one-dimensional search technique to reduce the interval of uncertainty for the…

A: Use the golden section search to find the value of that function: f=6.64+1.2x-x2 which maximizes in…

Q: Two nonnegative numbers whose product is 25a² (where a 0) and whose sum is a minimum, are

A:

Q: Find the global maximum and global minimum of f(x)=x22x in the interval [−1,3].

A: We first find the critical points by solving f'(x)=0

Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: Suppose that the FIRST DERIVATIVE of a function f is given by f' (x) = (x – 3)² (z² + 5x). Find the…

A: We find the critical numbers by solving f'(x)=0

Q: Show that 1/2 is an eventually fixed point for

A: T22 or T12 That can be proved as it will have the 12 in the equation, for any fixed point .

Q: Find the points of local minimum and  local  maximum of the functions f(x) = sin2x where x belongs…

A:

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: Find the equation of the tangent line to the graph of the functic f(x) = 3x² - 4x +5 at the point…

A: Find out the equation of tangent line.

Q: . How many point(s) of inflection are on che graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x² -…

A:

Q: The function f(x) = 2x°- 36x+210x + 4 has one local minimum and one local maximum. Use a graph of…

A:

Q: 3) y =x² +2x - T 4) y=x² – 8x + 14 2.5 1.5 0.5 -1 -0.5 -3 Find EXACT Vaiue's of x- intercepts For…

A:

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: 3. The graph of f(x) = 3(x – 2)² – 6 is a parabola that opens %3D with its vertex at (L, -), and…

A: The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If…

Q: Find the absolute extremd of the on the closed interval. 6x2 g(x) (-2, 1) X - 2 minimum (x, y)…

A:

Q: Sketch the graph of a function that has neither a local maximumnor a local minimum at a point where…

A: Sketch the graph of a function that has neither a local maximumnor a local minimum at a point where…

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 two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

Q: Sketch the graph of a function that has a local maximumat 2 and is differentiable at 2.

A: We have to sketch graph of function that has local maximum at 2 and is differentiable at 2. We know…

Q: Create a quadratic relation such that the relation passes through point A(x,y) and contains a…

A: To create a quadratic relation such that the relation passes through a point and contains a vertical…

Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

A:

Q: Find the global maximum and global minimum of f(x)=2x in the interval [−1,3].

A: Given function is Differentiating with respect to x, we get Now, f'(x) =0 for no value of x and…

Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Determine the maximum number of turning points of f. 6. f(x) = (x – 2)2(x + 4)2 7. Identify the end…

A:

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: Differentiate the given function with respect to x and equate it to zero,…

Q: Find a cubic function whose graph has a relative minimum at (0, 1) and a relative maximum at (3, 5).…

A:

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

Q: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

A:

Q: Suppose the graph of f(x) = x3is compressedvertically using a factor of 1/3and then shifted to…

A: Given : The parent function is f(x ) = x3 . The graph of f(x) = x3 is compressed vertically using a…

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: The absolute minimum of f(x) =x² – 4x On [0,3] is y= %3D 540 .BO -4 .CO -3

A: We use first derivative test to find absolute minimum.

Q: Sketch the graph of a function on [-1, 2] that is discontinuous but has both an absolute maximum and…

A: There are many ways to draw the graph with given conditions. One such a graph is as shown below.

Q: Find the minimum and maximum of 1 on the interval [0, 3].

A:

Q: 1. Find two non-negative numbers whose sum is 12 such that their product is an absolute maximum.

A: Let x and y are two non-negative numbers. We have to find maximum of the function Fx,y=xy It is…

Q: Find the global maximum and global minimum of the function f(x)=x2−16x on the interval [−4,−1].

A:

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

A:

Q: graph of f(x) = 4(x – 2)² – 7 is a parabola that opens --Select- v with its vertex at (x, y) = ( and…

A:

Q: bounded by the graphs of the equat y

A:

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

A:

Q: Find the solution to the equation 2x² - 4x + 1 = 0 using simpsons rule with an lower a and upper…

A: Given , f(x)=2x3-4x+1 we have to use Simpsons rule to find solution with lower limit is 1 and upper…

Q: Where are there local minimum(s)/maximum(s) f(x)=3(2x-1) -4(x+1)?

A:

Q: What are the absolute maximums and minimums of z(x) over its domain?

A: Given To find what are the absolute maximums and minimums of z(x) over its domain.

Q: Find domain and range of the funetion f(x, y) In[e-x' -y'1

A: The ln function is undefined for negative arguments. This will ensure that argument is positive. So…