Suppose that f(3) = 1, f(3) = 2, and f"(3) = -4. (a) Which of the following graphs most resembles the graph of y = f(x) close to x = 3? %3! (b) The equation of the tangent line tof at 3 can be written as y = mx + b. What is the value of m? (c) The equation of the tangent line to f at 3 can be written as y = mx + b. What is the value of b?

Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

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

A: To find the slope we find y' at x=0, y=0

Q: 8. Find all points on the graph of y = (x + 3)² at which the tangent line is parallel to the line…

A: The given graph is y = (x +3)2 To find the points on the graph at which tangent is parallel to the…

Q: Find an equation of the tangent line to the graph of the function at the given point. ex + e-X y = 7…

A:

Q: 5. Find the equation of the tangent line that passes through point (1,2) to the graph 8y3 + x²y – x…

A: Proceed as shown below...

Q: Find h'(-2) if h = f • g, f(x) = -6x2 – 4 and the equation of the tangent line of g at -2 is y = -9x…

A: Slope of y=-9x+6 is = -9 This line is tangent to g at x=-2  So we get: g'(-2)= -9   The tangent line…

Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

A:

Q: 1. Find an equation of the tangent line to the graph of f (x) x+8 at (1/2, -17). x-1

A: The required equation of the tangent line to the graph is y = -36x + 1

Q: 4. Find the equation of the tangent line to the graph of g(x) = v2-x at x =-7 %3D

A:

Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: what would the equation of the tangent line to the graph of y=(4x^4-3x-1)/(3-x^2) be at x=1

A:

Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: 4. Find the equation of the tangent line to the function y= In(x* -2) when x=3.

A:

Q: 3. Find the equation of the tangent line to the curve y = x2 - 3x + 4 that perpendicular to the line…

A: we have to find the equation of the tangent line to the curve y=x2-3x+4 that is perpendicular to the…

Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: Find an equation of the tangent line to the curve atthe given point. y= In (x3 - 7) , (2 ,0)

A:

Q: y = x^2+ 1, find an equation of the tangent line to the graph of y at x = 3.

A:

Q: -1 Where on the curve y = (256+ x²)¯* does the tangent line have the greatest slope? NOTE: Enter the…

A:

Q: Find an equation for the tangent line to the graph of y – 3xy + x2 +1 = 0 at the point (2, 1).

A:

Q: Find the equation of the tangent line to the graph of ƒ(x) = 4/x at x = 2

A:

Q: 1. Find the equation of the tangent line and normal line to the graph of y=√x² +3 at the point (-12)

A:

Q: Find the equation of the tangent line to the graph of y = 2x - (4 / √x) at the point (4, 6).

A: Given,            y = 2x - 4x and Point is 4, 6

Q: Find an equation of the tangent line to the graph of Y = e2x-3 at the point (3/2,1).

A:

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: 18. At what point on the graph of f(x) = 2xe" is the tangent parallel to the line with equation y=…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 2. Find the equation of the tangent line for the function 2 f(x) = x2 + - 3 at a = -2

A:

Q: 19. If an equation of the tangent line to the curve y = ƒ(() at the point where a = 2 is y = 4x - 5,…

A: The given equation of  tangent line at curve y=f(x) at a point is y=4x-5. Now, at point a=2 tangent…

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: 9) If f(x)= x' – 3x, find the equation of the tangent line at x = 2.

A:

Q: Find the equation of the tangent line at the point (1,−1) to the curve defined implicitly below. x6…

A: Given equation of curve x6 + y2 = 2let the tangent line be y = mx+c where m is the dy/dx and c is…

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

A:

Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 4 if g(4) = −3 and g'(4) = 6.

A: Given that  y=g(x) and g(4)=-3 also g'(4)=6  We have to find the equation of tangent line . Please…

Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

A:

Q: 4. Find the equation of the tangent line to the graph of x3-3xy+ y2 +19 =0 at the point in the…

A:

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

A:

Q: 7. Find the slope of the tangent line to the graph at (1,1): x2y? - 9x2-4y2 = 0 x-9-4-0 (-4, 2/3)…

A: x2y2−9x2−4y2=0 Use implicit differentiation to find the slope of x2y2−9x2−4y2=0 Implicit…

Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: 4. Find the equation of the tangent line to the curve f (x) = (x² – 4)(2x + 1) at x : -2.

A:

Q: 1 Find an equation of the line tangent to y at point (0, -). X-3

A: Given y=1x-3 at point 0,-13 To find equation of line tangent:

Q: 3 PROBLEM 2:f(x) at (-1,3) x+2

A: topic - slope of a tangent line

Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

A:

Q: Find the equation of the tangent line to the graph of x^2y-xy^4=-1830 at (3,5)

A:

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

A: Given, fx=4xx2+6 Now we find the slope ddx4xx2+6 Now by using the quotient rule,…

Q: x3+6x-2 dx x4+6x2

A:

Q: 4. If f (2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

A: We have to find the equation of tangent.

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

A:

Q: 7) Find the equation of the tangent line to the graph of f(x) = –sin(x) +3 at x = 4

A:

Q: If 2x2 + 5x + xy = 4 and y(4) = -12, find y (4) by implicit differentiation. y (4) = Thus, an…

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.