that is tompent ☺ Find the equation to the the Cime curve of fG)= (4-3)9 at x =l 4 (Tes f(x) = (4-3x) at x =1 %3D

Q: 8) Find all values of t for which x = +5, y = t lnt – t has a vertical tangent line

A:

Q: Find the equation of the tangent line to the curve f(x) = a² + 2x at x = 1. Enter the answer in the…

A: f(x) = x2 + 2x      at x=1  y = x2 + 2x   At x=1  =>  y = 12 + 2(1) = 1 + 2 = 3 point on the…

Q: y = 7x + e5x ; (0, 1) %3D

A:

Q: 4 Find all the points on the curve x2 + xy + y? = 3 where the tangent to the curve is a vertical…

A:

Q: Q.1. Justify why the level curves very close to the origin (0, 0) for the function f(r, y) =…

A: To find the level curves, equate the function fx,y with a constant C.

Q: The graph of y = f(x) (solid curve) appears below, together with the tangent line %3= to the graph…

A: Given graph of y = f(x) with the tangent line to the graph at (2,0.5) is, To estimate f(2.5)

Q: 3. Find the equation of the tangent line to the graph of y at the point (1,0) given 2r² where r> 0.…

A: Given that: xy+1x2=2x2+y

Q: -2x²+2x+1 Find the equation of the tangent line to the graph of F(x) ev dy at x = 0. sech z

A:

Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

A:

Q: Find the question of the that is tangent to the curve y=-3 cos2x at x= n/6. Express with exact…

A:

Q: The equation of tangent line to the graph of 8x²+16y²=48 at (2,1) is A x- y - 3=0 x- y+3=0 c none of…

A: Slope of tangent line is y'

Q: 3. Find the slope of the tangent at x = 1 for y = ln(2x + 3) a) 2 b) = d) In(5)

A: As per Bartleby guidelines rule I am answering only first question as both question are different…

Q: find the tangent to the curve f(x)e%*-2% at X=-1. Express answer exactly in terms of e (not a…

A:

Q: ngent line to the curve y= In(x4 + 1) at x

A:

Q: 3) Find an equation of the tangent line to the graph of y = (z + 4)² at z = 4.

A:

Q: 12. Find the x-coordinate of the point on the graph of y= Vx where the tangent line is parallel to…

A: From the given data: x=1 x=4

Q: Determine the slope of the tangent line to the curve y = In(x²) at x = e 2 1 e4 Option 2 Option 3 1

A: differentiate it with respect to x at given point to get the slope of line.

Q: 8. Find the equation of the tangent line to the curve y = e* at the point (a, f (a)) when a = In 3.

A:

Q: Find the equation of the tangent line to the curve y=4+e2sinx at the point (0,5).

A: our objective is to find the tangent line equation.

Q: What is the slope of the tangent line that touches the graph of In y + e2z-1 = 3y – 4x at the point…

A: Given that: lny+e2x-1=y-4x

Q: 3. Find the equation of the tangent to the curve 3xy-y²= 7 at the point (.1).

A: Follow the procedure given below.

Q: Find a > 0 such that the tangent line to the graph of f(x) = x 2e-x at x = a passes through the…

A: fx=x2e-x Differentiating with respect to x, we get f'x=dx2dx·e-x+de-xdx·x2=2x·e-x-e-x·x2=x e-x2-x…

Q: What is the equation of the tangent line to graph of the function y = e^(3x) at the point (0,1)? O y…

A: The given function is y=e3x

Q: Find the slope of the tangent line to the graph r=2sin(0) at the point V3, 3 11.

A: We have to find

Q: Does the graph of Sxsin(1/x), x + 0 g(x) 1o. x = 0 |have a tangent line at the origin? Give reasons…

A:

Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT TH INDICATED POINT. 4.…

A: we only solve one problem at a time, please upload it one by one

Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

A:

Q: Find an equation of the tangent line to the graph of y=e^-x^2 at the point (2,1/e^4)

A:

Q: d the equation of the tangent line to the graph at the specified value of x. y=x√3-x², z = 1.

A: Given query is to find the equation of the tangent.

Q: . Find an equation for the tangent to the curve x sin 2y = y cos 2x at the point (T/4, 7/2). %3D

A:

Q: 1. If f(x) = (2x)cosx, then f'(x) =?

A: Dear student as per our rule in one session we can only solve one question please post the other…

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = V3x – 5

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: An equation of the tangent line to the curve y= cos(x) at a = T/3 is (- 7/3). %3D y =

A:

Q: A curve is defined implicitly by the equation x² + 3xy + y² = 1 Differentiate implicitly to find dy…

A:

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

A:

Q: 6. Find the equation of the tangent line to f(x)= = tan (2x) at the point (n/8, 1).

A:

Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

A:

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

A:

Q: -2x²+2x+1 Find the equation of the tangent line to the graph of F(x) evI dy at x = 0. sech my

A:

Q: Determine the equation of the tangent line to the curve f(x) =xV x +1 at × =3. 11 A 4 11 B 2/3 space…

A:

Q: (3) Find the equation of tangent to the curve given by x=d cos' o y=a' sin'e at point o- VE (x+ y)…

A: Given the equation of curvesx=a3cos3ϕy=a3sin3ϕ

Q: Find the slope of the tangent line to the curve y = g²+4r+7 at the point (0, 3). 7a+2 Determine da…

A:

Q: 16. XZ is tangent to circle O at point X and XT is a secant line. If the m <TXZ = 69, find the m XT.…

A:

Q: ne points on the curve y = x³ + 3x< – 9x + 2 where the tangent is hor と、 = x° + -

A:

Q: Find the equation of the tangent line to th graph of f(x) = 3 – |2 – a| at a = 1. Select one: Y = -x…

A: Given:  f(x)  =  3 - |2 -x|To Find :  Equation of tangent at x =1Now , first of all we define f(x)…

Q: find y in terms of X dy x²(1-x32*, curve Passes through (!.7) Solution is y= Please write neatly the…

A: Firstly, we can separate the equation. (i.e, Move all y terms to one side and all the 'x' term to…

Q: 13. Given the function f(x) = 4 + x? %3D Find the 8x + 2 equation of the tangent line to the curve 1…

A:

Q: 14. Find the point(s) of the tangent to the curve h(x) x3 5x2 – 8x + 3 with same slope 3 4 as 48x +…

A: first find the slope of curve h(x) then find the slope of line. Therefore equate both slope in the…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.