2. Let f(x) = 2e# – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x) at x = 1, a = 2, and I = 3, and calculate their slopes. 4 - 2 - 4 -6 - 8

Q: Find the derivative using the following information.

A: Equation of tangent to curve g(x) at x=2 is y=-3x+2. Its slope is m=-3. Since slope of tangent to…

Q: 3. Determine the value of b if the slope of the tangent to f(x) = (3x² + 1)(2x² + b) at x =– 1 is –…

A: given,       fx=y=3x2+12x2+b    slope of the tangent, at x=-1      dydx=-16

Q: 1. Find the slope of the tangent line to the graph of f at x = 4, given that f(x) = -x2 + 4Vx.

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

Q: 21. Find an equation of the tangent line to the graph of f(x) = x² - 2x at (a) (–2, 8); (b) (1, –1);…

A: fx=x2-2x

Q: (3) Find the equation of the line tangent to f(x) = 2x³ - 2x2 +1 at x = 1. [Hint: f'(a) is the slope…

A: We find the slope of f(x) at x=1 by finding f'(1)

Q: B. Find the general form of the equation of the tangent line to the given curve at the indicated…

A:

Q: 1. Determine the points where the slope of the tangent to the curve: a. f(x) = 1- 3x² is equal to 5…

A:

Q: 2. Let f(æ) = 2e* – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: Graphed the tangents using a graphing calculator.

Q: Find the slopes of the tangent lines to the graph of f(x) = 2e² at the points (0, 2) and (1, 2e).

A: See the attached file to know how to find thesthe of a tangent at the given points.

Q: What is the slope of the tangent line that touches the graph of In(y) +e-=3y– 4x at the point A В) з…

A: slope , m=dydx.

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

A:

Q: 5. Find the slope of the tangent to the function b hor-0-s1= -S= xb 6 Ⓒ-(²-x) at x=1 Yo For-V xb

A:

Q: Find an equation of the tangent line to the graph of f (z) = -2² + 3z – 2 at the point (2, 0)

A:

Q: 8) Find the slope of the tangent line to the graph at the given point. (x² – y³)² = 4x²y - 3x -…

A: Consider the equation and the point

Q: Let f(x) = V13 – x The slope of the tangent line to the graph of f(x) at the point (4, 3) is The…

A: Given ,  f(x) = √(13 - x) (A)  We have to find the slope of tangent line to the graph of f(x) at the…

Q: 1 Find an equation of the tangent line to the graph of f(x) = c) at a) at (1,1); b) at 3, '27

A: Given - A Function To find - Its tangents at given points

Q: 34. Find an equation of the line tangent to the graph of f(x) = (2x – 1)(x + 4) at (1, 5).

A: The objective of the question is find the equation of tangent at the point (1,5).

Q: 22. Find an equation of the tangent line to the graph of f(x) = 4 - x² at (a) (-1,3); (b) (0, 4);…

A: Given: f(x)=4-x2 To Find: the equation of the tangent line to the graph at a) (-1, 3) b) (0, 4)…

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

A: As per guidelines we have to solve the 1st one

Q: 1) Find the equation of the line tangent to the graph of f(x) = (x² + 1)(x³ + 1) at the point where…

A:

Q: 4. At what point on the graph of y = ÷x² is the tangent line parallel to the line 2x – 4y = 3? A.…

A:

Q: 1) Find the tangent slope to the curve f_((x))=1/ (2x-1) at x=1

A: Given : fx = 12x-1

Q: 5. Find the slopes of the tangent lines to 2x? – 3xy+y³ = -1 at y = - 3.

A:

Q: [1] Let f(x) = x – 4.x³ + 3.x² – 4x – 4. Find the equation of the tangent and normal line to the…

A: We have to solve the problem

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: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

Q: 1. Find the slope of the line tangent to the graph of f (x) = x³ In (x² – 5x + 7) at x = 2. - Do NOT…

A: We have to find slope to given equation by derivative.

Q: What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the point.12

A:

Q: 49. Find an equation of the tangent line to the graph of y = 8/(x² + 4) at (a) (0, 2); (b) (–2, 1).

A:

Q: 4 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph of…

A: We know that if m is slope and (x1,y1) is point on line the equation of line is given as-  (y - y1 )…

Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

Q: 1) Find the slope of the tangent line to the graph of f(x) = x2 - 3 at the point (2, 1). %3D (8…

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: 3. Given that the graph of f passes through the point (2,5) and that the slope of the tangent line…

A:

Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

A:

Q: 4. Find the equation of the tangent line of the graph of f(x) = 12/T – 16 at the point where the…

A:

Q: Find the equation of the tangent line to the graph of function at the given point. Y = 5+ 1n(1-4x) ;…

A:

Q: determine the constants a and b so that the line y = -3x + 4 is tangent to the graph y = ax^3 + bx…

A:

Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: 2х — What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the…

A:

Q: Finding derivative.

A: Given,

Q: Find an equation of the tangent line to the graph of y = g(x) at x = –1 if g(-1) = 5 and g' (-1) =…

A: Concept: The Equation of tangent to the graph y = g(x) at point (x1,y1) is given by: (y -y1) =…

Q: Find an equation of the tangent line to the graph of the function f(x) = 4x – 2x3 at x = -1. Select…

A: Given: fx=4x-2x3   at x=-1

Q: Suppose f(5) = 2, f'(5) = 8, and g(x) = In [f(x)+4]. Find an %3D equation of the tangent line to…

A:

Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1.…

A:

Q: 3. Determine the value of b if the slope of the tangent to f (x) = (3x² + 1)(2x² + b) at x = – 1 is…

A: The formula to find the slope of the tangent to the function f(x) is f'(x).

Q: 3. Find the equation of the tangent line to the graph of x²y + 9xy= 162 at the point (-3, 6).

A:

Q: 5 7. Find the slope of the tangent line to the graph of y = x² at the point where x = –

A:

Q: Find the slope of the tangent line to the graph of the function at the given point. y = In x3 y 5E 4…

A: