Find the points of inflection of the graph of the function. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) f(x) = 6x – x2 (х, у) — (x, y) = %3D Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave upward concave downward

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Q: Q4) f(x, y) = x"/s –x/ay² Does the function is harmonic ?

A: If a function satisfied Laplace equation then the function is called harmonic function

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A: To find the direction in which the function is increasing most rapidly.

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A: f(x) = sin(x2)                                       [0,4π]f'(x) = 12cos (x2)f"(x)  =-14sin…

Q: (b) Find the value of k for which 2y +x k is a tangent to the curve y +4x 20. %3D

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A: Simple solution for differential equation....

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A: Given that, graph of function  y=x   We have to find Point P on y which is closest to (4,0)

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A: To calculate the approximate value of a) f(1.9) and b) f(2.04)

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A: See the detailed solution below.

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Q: find the specific function values. ƒ(x, y) = x2 + xy4 ƒ(-1, 1)

A: Given: fx,y=x2+xy4, f-1,1 for finding given value we substitute x=-1, y=1 in given expression

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A: Concept - take the derivation on both side with respect to x

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A: Inflections points are those points at which second derivative is 0.

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A: Given,

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A: We have to use integral formula.

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A: Given function is fx=2x3-9x2-60x-3. Compute the derivative. f'x=2x3-9x2-60x-3'=6x2-18x-60

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A: Given function fx=x3-6x2+23x-30 and f is concave upward f''>0and concave  downward f''<0

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Q: Find the smallest positive c for which (c,0) is an x-intercept for the function f(x) = tan(1.46x).…

A: The given function is: f(x)=tan(1.46x) To find the smallest positive c for which (c,0) is an…

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Q: 1. For the square root function f(x) = V, (a) calculate an equation for the secant line connecting…

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Q: Find the exact value of fo f(x) dz for the function f(x) graphed below.

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.