A.Find the linear approximation of the function  f(x) = Radical(4-x)at a = 0. B.Use L(x) to approximate the numbers Radical(3.9) and Radical(3.99). (Round your answers to four decimal places.) C.Illustrate by graphing f and the tangent line.

Q: The slope of the tangent line to the graph of the function y = 2/x – 6 at (36, 6) is 6 -0.50 0.17…

A:

Q: Find an equation of the line L tangent to the graph of f(x) = 8x +1 at x = 1/2.

A: Calculate the y-coordinate of the point where the tangent has to be drawn. Substitute 12 for x in…

Q: Find the line tangent to the graph of f(x) = x² + x +1 at xo = 2

A:

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

A:

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

A:

Q: Find the equation of the tangent line to the graph of f (x) = -4e2* at the point (0, -4). Hinti Sh

A: Explanation of the answer is as follows

Q: Q1. Write down the linear (tangent line) approximation to y = e x / 2 at the point x = 0, and…

A:

Q: 4. Write an equation for the line tangent to the curve f(x)=" In(3x) -at x=1

A:

Q: Find the slope of the line tangent to the curve x - 3xy + 4x = 2 at x = 1. -5/3 O 2/3 O 1/3 O 4/3

A: The given curve is: x3-3xy+4x=2 We need to find the slope of the line tangent to the given curve.…

Q: Find an equation of the tangent line to the graph of the function at the given point , f(x) = e3x,…

A: Equation of the tangent line: y - y1=m(x - x1) m=f'(x)

Q: Find the equation of the tangent line to the graph of the function g(x)=2x-1/3x+1 at x=0.

A:

Q: Find the equation of the tangent line to the function f(x)=2x^2−9 at the point where x=−6. Give your…

A: Calculate the derivative of the function at given point than write the equation of tangent line.

Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1.

A:

Q: Find an equation of the line tangent to the graph of the function: f(x) = V2x² – 1 at point P(-1;1).

A: Given:- f(x) = (2x2-1)(1/3)  To find:- Equation of tangent line at point p(-1, 1) on given curve

Q: Find the equation of the line that is tangent to the graph of the functio f(x) = x+1 at the point T…

A:

Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: 5. Find an equation of the tangent line to the graph of f(x) = In (2x + 1) – e* at the point where x…

A:

Q: Write an equation of the tangent line to the graph of f(x) 3x at x = +1. %3D 1+2x2 For what value(s)…

A: Given that fx=3x21+2x2 Solution :fx=3x21+2x2f'x=6x1+2x2-4x3x21+2x22if…

Q: Find the equation of the tangent line to the function f(x)=-3x^2-2x at the point where x=1. Give…

A:

Q: Find the equation of the line tangent to the curve x^3 - 3xy + 4x = 2 at x = 1.

A: On solving this we will get

Q: Find an equation of the line tangent to the graph of f at the given point.

A: Solution:Given          f(x)=sec-1(ex);              (ln 2, π/3)To find the equation of the line…

Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = - 1- 2x Provide your…

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. 1 f(z) = at…

A: Given function :                   f(x)=1x2-2x+9   At the point :  (2, 13)   To determine:…

Q: Determine the value(s) of x for which f(x)=9x+8 has a horizontal tangent line.

A:

Q: If y=mx+b is the equation of the tangent line to the graph of f(x)= x² - x at x= -1, then m=

A:

Q: Suppose that f(x)=4x(1−5x)^4 Find an equation for the tangent line to the graph of ff at x=2

A:

Q: Find an equation for the line tangent to the graph of f(x) = 2xe %3D at the point (a, f(a)) for a =…

A: f(x) = 2xexslope of tangent will be calculated by differentiation function f(x) at given point.f(x)…

Q: Find the slope of the tangent line to the graph of the function at the given point. 4x? + 3y² = 36…

A:

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

A:

Q: Find the equation of the tangent line to the graph of the function f(x) = (22 +6) (z – 3) at the…

A: Fund the equation of the tangent line.

Q: Find the equation of the tangent line to f at x = a. f (x) = 3 − 4x,             a = 2

A:

Q: b) Determine the equation of the tangent line to the grap f(x) = 2x² – x + 5 at the point where x =…

A:

Q: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

A:

Q: Determine the value(s) of x for which f(x) = 9x + 8 has a horizontal tangent line

A:

Q: a. Compute the derivatives of the following function: sec(xy) = 4x(3x+ 5)5 b. Find an equation for…

A: Product Rule of differentiation : d(u.v)dx=u.dvdx +dudx.v dxndx = nxn-1 Equation of line passing…

Q: Find the equation of the tangent line to the function f(x)=x3+3x2+x+4 at the point where x=−2. Give…

A: we have to find tangent line at x=-2given

Q: 2. Find the equation of the tangent line to the graph of f(x) = 3x?e-1 - 1, at r = 1.

A:

Q: If y=mx+b is the equation of the tangent line to the graph of f(x) = X .2 - X at x= -1, then m= b3D

A: According to power rule of differentiation

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = 3 1- 2x Provide your…

A: see below the answer and explanation

Q: Use this formula to find the slope of the tangent line to the curve at the given x-value. f(x) =…

A:

Q: Find the slope of the line tangent to the graph of f(x) = -x-1 at x = -3. Provide your answer below:…

A:

Q: Let f(x) = 2x* + 3x° + 10. Find the equation of the line tangent line to the graph of Y point (1,…

A: Given  f(x) = 2X⁴ +3X³ +10 We need to find the equation of tangent of f(x) at the point (1,15)

Q: Find the equation of the tangent line to f(x) = (36 + 4x²)¯ at x = Use your answer to (a) to…

A: (a) Given,              f(x)=(36+4x2)-12       at  x=0.

Q: Find an equation of the tangent line to the graph of the function at the given point, y = e3x−x2,…

A: Given equation: y=e3x-x2 The equation of the tangent passing through the point x1,y1 on the curve…

Q: Find the equation of the tangent line to the graph of f (x)= 3e* +1_where x, = In 2.

A: As a first step we need to find the derivative of f(x) at the given point.

Q: Find the equation of the line tangent to the graph of f(x) = (In x)* at x=7.

A: Slope is evaluated by differentiating f(x) wrt x at x=7 . Also f(7) is evaluated. Write equation of…

Q: The slope of the tangent line to the graph of the function y = 8/T- 4 at (16, 28) is O 4 O -1.75 O…

A: Slope : It is the Differentiation of y with respect to x at a given point.

Q: Find an equation of the tangent line to the graph of the function h(x) = −xe2−x, at the given point…

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: For the function y= In(x² – 2) , the slope of the tangent at x = 2 is

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: