Using the function y = (x2-1)2 a. Find the interval of concavity b. Find the point of inflection/s

Q: Find the maximu rate of change of the function f(x, y) = x2 + xy+y at the point (-8, -7). V1013 3114…

A:

Q: find extreme Value of function fex, y) = x°t 3xy?-3x²-3y=t7 1

A: Given:  fx,y=x3+3xy2-3x2-3y2+7 ⇒fx=3x2+3y2-6x, fy=6xy-6y To find extreme points put fy=0, fx=0…

Q: Find the r value of the point on the curve y = 3x + 2 closest to the point (1,0). Evaluate /(-글 +…

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

Q: Q5: Does any tangent to the curve y vx cross the x-axis at x--1 If so, find an equation for the line…

A: It is required to find if any tangent to the curve y=x cross the x-axis at x=-1. First find the…

Q: x = t3 − 12t,    y = t2 − 2 find d2y dx2 and for which values of t is the curve concave…

A: We find dx/dt and dy/dt.

Q: Find an equation for the line tangent to the graph of f(x)=4xe square root of x at the point (a,f…

A:

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

Q: JA di is concave downward. Find the interval on which the curve x) - 6+ 8t

A:

Q: S(r) = x – 2:r +4 What is the y-intercept of the tangent line that intersects the function at I= 2?…

A: We know that,The tangent point of the given curve can satisfied the equation of that curve.

Q: Q6. Find ranges of values of x for which the curve y = x* +8x - 126.x² – 11x +187 is concave upward…

A:

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A:

Q: The tangent to the function, f(x) = -2x² + 3 at the point (-1, 1) is the hypotenuse of right…

A:

Q: Consider y = xe^x on the interval [-5, 0]

A: In order to find global minima of the function, check the values of the function at end points and…

Q: r(y) = Vy? – 6y ,2 бу

A: Consider the given function as ry=y2-6y5 Simplify as ry=y2-6y15

Q: Find the interval(s) where the function y = x – 2x² – 7x + 2 is concave down. Justify your answer.

A: Find the double derivative of y and then equate it to zero.

Q: Find all values of x at which the tangent line to the curve 2x + 11 is perpendicular to the line y =…

A: Graph and tangent line

Q: (7) For the function f (x) = 0.25x - 2r3 Find intervals of concavity and inflection points

A: From  first derivative and second derivative of the given function we can answer to this question.

Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: V4 – x2 – y? In(y – x) - Find and sketch the domain of f(x, y) -

A: Given,fx,y=4-x2-y2lny-xRoots are:y=-4-x2y=4-x2Domain is: (x,y)∈R2:log(y-x) ≠0 and x<y and x2+y2≤4

Q: 0. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

A:

Q: f(x) = between x = 2 and x = 9 using the "midpoint rule" with two rectangles of equal width.

A: Given function, f(x)=1x  bounded between x=2 and x=9 The lower limit, a=2 and the upper limit, b=9…

Q: 1. For the function f(x) = 2x? + 7x – 3, - (a). Find the slope of the tangent line at x = 2. [1Mark]…

A: The answers are : (a)  15  (b) y = 15x - 11   The detailed solution is as follows below:

Q: Find the slope in the x-direction at the point P(0, 2, f(0, 2)) on the graph of f when f (x, y) 3(y?…

A:

Q: (a) Define what it means by for y = f(x). %3D

A: In this question we have to define the meaning of dydx for y=fx

Q: What is the slope of the line tangent to the curve x2 + y2 = 1 and parallel to the x-axis ? OA…

A: what is the slope of the line tangent to the curve x2+y2=1 and parallel to the x axis

Q: Find an equation for the line tangent to the graph of  F(x)=6xe^x at the point (a,f(a)) for a =3…

A:

Q: For the function: f(x) = 2sin (G) on the interval [0,4Tt], find: Relative max = (t,[ ? ]) Relative…

A: This is a problem related to maximum and minimum of the function. Based on the general formula and…

Q: Find an equation for the line tangent to the graph of f(x)=4xe^x at the point (a,f (a)) for a=3…

A:

Q: Find an equation for the line tangent to the graph of f(x)=−2xe^x at the point (a,f(a)) for a=2.…

A: Find the derivative for f (x). Find f’(x) at x = 2.

Q: h of the function, y %3D bel your axes clearly. (x)103

A:

Q: w For what values of x is the tangent line of the graph of f(x) = 6x' + 27x² – 71x – 54 - parallel…

A:

Q: Given that y" = 2x, find the value of y when x = 3 if the curve passes through the point (-1,); and…

A:

Q: Find the x value of the point on the curve y = 3x + 2 closest to the point (1, 0).

A:

Q: -3. For the function f(x) = -5x - 3, find the slope of the tangent line at x =

A: We can find the slope in the following steps.

Q: Use the implicit to find the slope dx of the given function y2 - x3 = 41 at (2,-7)

A:

Q: Find the x-coordinate of the point where the curve y = x3 - x crosses the horizontal line y = 1.

A: Given:                                 y=x3-x and y=1  Let                                y=x3-x…

Q: O For what value of x does the function f (x) = 4x2 – x +1 have a horizontal tangent?

A:

Q: Q5: Does any tangent to the curve y = vx cross the x-axis at x=-1 If so, find an equation for the…

A: To find: The equation of tangent to the curve y=x if possible. Given: The equation of the curve y=x.…

Q: How do you find the domain and range for f(x,y) = ln(x+y)?

A: The given function:

Q: The inflection point of the curve x3 y = V7 -x² + 10x + 97 2 6

A:

Q: f(x)= x' -9x² +15x – 7 what is the tangent line slope which is drawn at the inflection point of…

A: The given function is f(x)=x3-9x2+15x-7

Q: Let f(x) = 3x² – 7x + 5. What is the value of x for which the tangent line to the graph of y = f(x)…

A:

Q: 8. Given the function f(x)%=2x3 -5x3 , find the point where the tangent is horizontal to the curve.

A:

Q: Q3) State the approximation for a differentiable function f(x): (a) V51 (b) V123 (c) (33)

A: (a) 51 Linear approximation is obtained as Lx=fa+f'ax-a Consider the function fa=a. On…

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

A:

Q: Find the point P on the graph of the function y= sqrt(x) closest to the point (6,0)The x coordinate…

A:

Q: Q4) r(x,y) = x'/s – ½y? is harmonic ? Does the function %3D

A: The given function isf(x, y)=x13-19x-53y2to check the function is harmonic?

Q: Q4: Find the distance from the origin point to the line x-2y-1 %3D

A:

Q: Q2)B/ Find the points on the curves y(X) given by y = x - 6x? + x+3 where the tangents are parallel…

A: