Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

Q: Find the equation of the tangent line to the curve f(x)= at the point (1, 1+x² -).

A: The equation of the tangent line: - The formula y – y1 = m (x – x1) can be used to find the equation…

Q: Find the equation of the tangent line at the given value of x on the curve. y° +xy² -61=x+3y°; x:…

A:

Q: Find an equation of the tangent line to y = 7 sin(x) at x =

A: Solution-  Equation of tangent is given by y = mx+ c ( where m is slope)    Given equation is  y = 7…

Q: Find an equation of the tangent line to the curve atthe given point.   y =  Sin (2 In x) , (1 ,0)

A: Given curve,  y = sin(2 ln(x))  We have to find the tangent line to the curve at the point (1, 0)

Q: Find an equation of the tangent line to y = xt + 2x2 – x at x = 2

A:

Q: Find the equation of the tangent line to the curve y = x Vx +5 at the point (2,6).

A:

Q: π Find the equation of the tangent line to the curve y= Jx² –sin-(4x) at x =-. 4

A: We are given the equation, y=x2-sin24x at x=π4. Here,           dydx=x2-sin24x'…

Q: Find the slope of the tangent line to x2y2+x sin(15y) = 4 at any point (x, y) on the curve.

A:

Q: 2 Find the equation of the tangent line to the curve y =xNx +5 at the point (2,6)

A:

Q: Find the derivative of y with respect to x if y = (7x - 14x+ 14) eX. %3D dx

A:

Q: Find an equation of the tangent line at the given point.…

A: The given function is,x2+sin y=xy2+1 , (1,0)

Q: Find the slope of the tangent line to the curve defined by 4x + xy – y* 1760 at the point (8, –4). e…

A: To find the slope of the tangent line to the given curve at the given point

Q: Where on the interval [0, 4] does ƒ(x) = 4x - x2 have a horizontal tangent line?

A: Determine the value for derivative of f(x) i.e f'(x). fx=4x−x2f'x=ddx4x−x2=ddx4x−ddxx2=4×ddxx−2xSo,…

Q: Find the equation of the tangent line to y = at 3 - x X = 1.

A:

Q: Find the equation of the tangent line to y = x2 at the point where x = 2.1.

A:

Q: What is the equation of the tangent line to the curve y= In(x“ + 1) at x=1?

A:

Q: Find the equation of the tangent line to the curve y = ex/x + ex at (0, 1).

A: Given that curve  y = exx+ex at (0, 1). The slope of tangent any point on the curve is given by its…

Q: Find the slope of the tangent line to the curve y3 + yx2 + x2 − 3y2 = 0 at the point P(0, 3) by…

A:

Q: Find the equation of the tangent line at the given point on the curve. 2y - Vx = 4. (16,2) y =U

A: We need to find equation of tangent line.

Q: Find the equation of the tangent line to the curve x4+y4=2 at the point (1,1)

A:

Q: Determine the equation of the line tangent to x² + sin y = xy² +1 at the point (1,0).

A: The equation x2+siny=xy2+1, we have to determine the line of the tangent at the point (1,0).

Q: The slope of the tangent line to f(x) = cos(x) · sin(x) at x - 2т is

A:

Q: Find the equation of the tangent line and normal line to the curve: 2. x2 + 2xy = y3 at the point…

A: Firstly, we find  dy/dx by differentiating both sides with respect to x

Q: Find an equation of the tangent line to the curve at the point (0, 1) y = e2x + sin 3x

A: Here is the solution of the given problem.

Q: Find the slope of the tangent to the curve y= 2 sin'x at x-

A:

Q: Find the equation of the tangent line to y = 2r5 - 3x³ at the point where x = 0.7, with coefficients…

A: Methods to find the equation of the tangent at a point helps to find the required answer to the…

Q: Find the equation of the tangent line on the curve defined by 2xy- y² =1 at x = 1. A y=x-1 B y=1 ©…

A:

Q: Find the equation of the tangent to y-cos 2x at the point 0. Oal y--2- Ob) y- 2x+ O) y--+1 O d)…

A:

Q: Find the equation of the tangent line on the curve f(x) = V5x + 6 at x = 2.

A: Proceed as shown below...

Q: Find the equation of the tangent line at the given point on the curve. 109y2e 327x/10. (10,3) , 3x2…

A: Given,

Q: Find an equation for the tangent line Y= 4x-since when x=0

A: To find the equation of tangent  line

Q: Find the slope of the tangent line to the curve x + xy – y = 23 at the point ( – 3, – 2). -

A: The given function is x2+xy-y3=23 The point is x0,y0=-3,-2

Q: 4. Determine the equation of the tangent line to y = x²sin2x, at x = - R

A: Follow the procedure given below.

Q: Find the equation of the tangent line to the graph of f(x)= x ln(2x+3) at the point (-1,0).

A:

Q: Determine the equation of the tangent line to f(x) = sin(x) at x = π/3

A:

Q: 2. Find the equation of the tangent line to y at x = -5.

A:

Q: Find the equation of the tangent line at the given point. 4x = -5xy + 4y at (1,–4) y = arccos(5x) at…

A: See the calculation below

Q: 2/ Find the equation of the tangent line at (0,0) to fex) = xex хе 2 -X

A: Given f(x)=xe-x2y=xe-x2Differentiate…

Q: Find an equation of the tangent line to y = 5 sin(x) at x 4

A:

Q: Find the equation of the tangent line to the curve at point (0, ln 2).   y=ln(e^x+e^4x)

A: the equation of the given curve is: y=lnex+e4x we have to find the equation of the tangent line to…

Q: Find the slope of the tangent line to x2y2+x sin (15y) = 4 at any point, (x,y) on the curve.

A:

Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

Q: The slope of the tangent line to the graph of xy = In(x² + y²) at the point (1, 0) is

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Find the equation of the tangent line at the given value of x on the curve. 2y° + xy - y = 16x*; x=1…

A:

Q: 3. Find the equation of the tangent line to f(x) = 2x · sin (x) at the point (5, ).

A:

Q: The slope of the tangent line to the curve 2xy + T cos y = 2n at point (1,“) is:

A: The given equation is 2xy+π cos y=2π and the point is 1, π2. Evaluate the slope  y' using implicit…

Q: Find the slope of the tangent to the curve y=(cos 3x)/( 2-ln(2x+1) ) at x=0

A:

Q: Calculate the equation of the tangent line to the curve x^2+xy+3x+2y-1=1 at the point (0,1)

A:

Q: Find the slope of the line tangent to the graph of y = sin-1 x at x = 0.

A: y=sin-1(x)

Q: Determine the equation of the tangent line to g(x) = sin(6x) at x = A.

A: Given ,  g(x) = sin(6x) at x = π  We have to find the equation of the tangent line  g(π) = sin(6π) =…

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.