Assume that f is a differentiable function where f(3) = 5 and f'(3) = 2. Find the equation of the line tangent to f when x = 3.

Q: Estimate the slope of the tangent line of the function f(x) = 2e* at the point x = e. %3=

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Q: Find the gradient of the tangent line to y when x = 2.

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Q: Determine the equation of the tangent line to f(x)=xx-1 at x=1. y=x y=x+1 x=1 y=1

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Q: Find the exact slope of the tangent line to sin (x) y = f(x) = 2x + S at the point where x = 2

A: we have the function y=f(x)=2x+sin(x)2 we have to find slope at point x=π6

Q: Find the equation of the tangent line to the function f(x) = e*-1 In(x + 1) when x = 0.

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Q: 3. Determine the slope of the tangent line to the curve f(x) = at (2x + 1)2 x = 1 by using the…

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Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: Determine the point on f(x)= 2x^e where the tangent is parallel to the line y= 2x-12

A: The equation of the curve is  f(x) = 2xe The line parallel to the tangent line on the graph of the…

Q: Evaluate the derivative of the function. y= sec "(2 In 8x) dx

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Q: Find the equation of the tangent line to f(x) =1 – x² at (1,0). -

A: here we use formula  y-y1=m(x-x1) at point (1,0)

Q: Find the equation of the tangent line for f (x) = 2 sec(z) at z = 6

A: To find out the equation of tangent line.

Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

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Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: Pls help ASAP

A: This question is related to equation of straight line, we will use differentiation to find the…

Q: What is the equation of the tangent line to the function f(x) = a? + 5x at the point (1, 6)?

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Q: Find the point where the tangent line to y = x* at x 0.3 crosses the x-axis. x-intercept =

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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: Use the definition of a derivative to find f'(0) where: x² sin () lo x + 0 f(x) If the derivative…

A: follow next step

Q: Find the equation of tangent line to the curve f(x) = 2 – dt 1+t at the point x = 1.

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Q: Find the equation of the tangent line to the curve f( x) = Assume f'( x) =- and x = 1.

A: Answer and explanation is given below....

Q: Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 3ex+7 f(x)= ?

A: Given:

Q: Determine the equation of the tangent line to the function y = 2 + xe³x + x when x is equal to 0.

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Q: Find the derivative of the funciton F(x) = dt. F'(x) =

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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: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

Q: Find the slope of the line tangent to f(x) = tan x at x=-. 4

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Q: Compute the derivative of h(sinx) at x = π,/6 , assuming that h' (0.5) = 10.

A: We have to compute the derivative of function hsin x at x=π6, assuming that h'0.5=10. We know the…

Q: Find the derivative of the function.

A: Given: y=ln(x4)(1,0)

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

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Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

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Q: Find the equation of the tangent line of f(x)=x−(1/x) at x =1.

A: Given function is fx=x-1x Above function can be written as y=x-1x. At x=1, y=1-11=1-1=0 So, given…

Q: Compute the equation of the tangent line to f (x) = sin(Tx) at x=0.5.

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Q: Find the slope of the line tangent to the curve y = sin' x at the point where x-x/3

A: We have to find the slope

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

A: Follow the procedure given below.

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

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Q: Find the equation of the tangent line to the curve f(x)= Va. Assume f'( x) 1 at x = 4.

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Q: Find the slope of the line tangent to the curve y = sin x at the point where x = 3

A: Given: y=sin5x To find: The slope of the line tangent to the curve y=sin5x at the point where x=π3

Q: The slope of the tangent line to √x+y+√√xy = 2y at the point (2,2) is:

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Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Find the derivative of f(x, y) = (2x – y°, sin(ry), r²y*)

A: Given f(x,y)=2x-y3,sin(xy),x2y3 differentiate f(x , y) with respect to x we get…

Q: Find the equation of tangent line to the curve f(x) = x² at x = 3.

A: Topic = Derivative

Q: e) Now, deduce the derivative of y = tan(r) by applying the Quotient Rule.

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Q: Use the definition of the derivative to find the equation of the tangent line to the graph of y = Vx…

A: We write 6x+3y=4 in y=mx+b form to find slope

Q: Find the equation of the tangent line to the curve f(x) = x³ln (x + 1) at the point (0, 0).

A: The given curve is: f(x)=x3 ln(x+1)

Q: Use implicit differentiation to show that the equation of the tangent line to the curve y²=kx at…

A: Given : y2=kx Therefore, y=k.x  .............................(1) Now, put (x0,y0) in the above…

Q: Find the slope of the tangent line to the curve y = 1/√,x at the point where x = 4.

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Q: Determine the equation of the tangent line to f(x) = x3 - x, at x = 1

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Q: Find the equation of the tangent line to f(x)=-2sin(x) at x=0

A: We have to find the equation of tangent line

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.