Question 6 (-. ) Given f(x) = |x – 1|+ x² and g(x) = x² + 1. 1) Find the secant line forf on the interval [0, 2]. 2) Find the tangent line to the graph of g at the point = 1.

Q: 1 Show that f'(x) : COs x + 1 Find the point(s) on the graph of f(x) where the tangent line have a…

A: Given : f(x) = 1 - cos x1 + cos x

Q: 8. [6 points] Sketch the tangent lines to the curve at the points where x = 2 x = -1 X = 1

A: Given : The graph is given  Tangent lines : x = 2 x = -1 x = 1

Q: The point (1,2) is on the curve y=f (x), and at any point (x,y) on the curve the tangent line has a…

A:

Q: Compute f and find an equation of the tangent line to the graph at x = a. f(x) 13x3, a 5 (Use…

A: Given function f(x):

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y) at the point (1,…

A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

Q: Find an equation of the tangent line to the curve at the given point. xy + x²y² : = 42, (6, 1)…

A: Given curve, xy+x2y2=42               ....1 And point (6, 1)

Q: The function y = sin x completes one period on the interval 30, 2π4, the function y = sin 2x…

A: Consider the function y = sinx and its Graph:

Q: 1. Verify Rolle's theorem for the function (x+2)' (x-3)* in the interval [-2,3]. Plot the curve…

A:

Q: Find the equation of the tangent plane to the graph of 7y f(x, y) = at the point (4, –1). (Use…

A: We will find the first order partial derivatives and use the formula to find the tangent plane to…

Q: Let F(x) be a function whose derivative F' (x) = f(x) is graphed below: -3 -2 3 6 --1 = -11.75,…

A:

Q: The tangent line to the graph of y = g(x) at the point (2, 8) passes through the point (1, 4). Find…

A:

Q: 5) Prove that the function y = tan x has no horizontal tangent lines. Do NOT show me a graph as a…

A:

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4,-7). (Use…

A: Topic:- application of derivatives

Q: Find an equation of the tangent line to the curve at the given point. xy + x?y? = 12, (3, 1)…

A: Equation of tangent line to the curve: Curve is :                      xy+x2y2=12 at (3,1)…

Q: Assume that functions f and g are differentiable with f( - 5) = 2, f'(- 5) = 4, g(- 5) = 3, and g'(-…

A:

Q: Uncover the function f shown that the slope of the tangent line to the chart of f at any point (x,…

A:

Q: Find the equation of the tangent line to the graph of the function f (x) = sin (3,/7) at the point…

A: To determine the equation of the tangent line.

Q: Find the point of inflection of the graph of the function. f(x)=sin x/2, [0,4 3.14]

A: First we will find it's first derivative then take first derivative is equal to 0 for finding it's…

Q: Question 4 please

A:

Q: In the given question, consider the function on the interval ( 0, 2π) (a) Find the open intervals on…

A: f(x)=sinxcosx+5 in 0,2π

Q: Find an equation of the tangent line to the curve at the given point. xy + x²y? = 56, (7,1) (Express…

A:

Q: 10 The point (1,f(1)) lies on the curve f (x) 5-3x a) If Q is the point (x, ƒ(x))find the slope of a…

A:

Q: 11) We defined derivatives using a secant line to estimate a tangent line. In the definition, what…

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. You must write…

A: Equation of tangent line of the function y=f(x)  at the point (a,b) is y-b=f'(x)x=ax-a

Q: Find an equation of the tangent line to the graph of function f(x) = 5Vx at the point (6,5 V6). %3D…

A:

Q: Find the equation of the tangent plane to the graph of 5y f(x, y) at the point (4, -7). (Use…

A:

Q: Find the equation of the tangent plane to the graph of G(u, w) = – cos (uw) at the point (5. ). (Use…

A:

Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)=−2sin x…

A:

Q: The curves f(x) = x² – 3x – 4 and g(x) = 2x – 10 intersect at the point (2,-6). Find the acute angle…

A: Given:     f(x) = x2 - 3x - 4      g(x) = 2x - 10  Intersect point : ( 2 , -6 )

Q: The tangent to the graph of f(x) = 1/x^2 at point (2, 1/4) form a triangle. Find the area of the…

A: Given query is to find the area of the triangle formed by tangent.

Q: Compute f' and find an equation of the tangent line to the graph at x = a. f(x) = 5x-3, a = 5. (Use…

A:

Q: 1 Find an equation of the tangent line to the graph of g(x) =2--x at the point (2,0). Write the…

A: To find the equation of tangent.

Q: arbitrary point on the graph of Describe the tangent line at an y = 2x + 8.

A: Given the equation of graph y=2x+8. We need to describe the tangent line on any arbitrary point on…

Q: The tangent line to the graph of y = g(x) at the point (9, 1) passes through the point (4, 6). Find…

A:

Q: The line x+ 3D2 is a tangent line to the graph of x + =2 at the point Select one: OA(-1,-2) о в.…

A:

Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

A: The given function is f(x,y)=ln17x2-14y2 and the point is 1,1. The equation of the tangent to the…

Q: 3. If f(3) = 2 and f'(3) = -4, find an equation of the tangent line when x = 3. %3D %3D

A: Given : f3 = 2f'3 = -4

Q: Find the equation of the tangent line at the given point on the following curve. 3 3 In (x+y)=x y" +…

A: The given equation is  ln(x+y)=x3y3+ln(x2+2)-8, (1,2).

Q: Find the equation of the tangent line to the graph of the function f (x) = sin (7/E) at the point…

A: The equation of line that passes through the point x1 , y1 and have a slope of m is defined by the…

Q: The curves f(x) = x² – 3x − 4 and g(x) = 3x - 9 intersect at the point (1,-6). Find the acute angle…

A:

Q: Consider the curve, x² - y² + sin (TX) In(x) + x = 0. =

A:

Q: The curves f(x) = x² – 2æ – 5 and g(x) = 4x – 10 intersect at the point (1,-6). Find the acute angle…

A: Given data: The expression for first function is f(x)=x2-2x-5. The expression for the second…

Q: 5. Carefully explain why 2 arcsin(x)+2 arccos(x) : Hint: How can we tell a function is constant from…

A:

Q: Let f(-3) = -7 and f'(-3) = -2. Then the equation of the tangent line to the graph of y = f(x) at x…

A: To find the equation of the tangent line

Q: (5,2). Find the equation of the tangent line to the curve y = 2 sec x 4 cos x at the point The…

A: Given:     y = 2 sec x  - 4 cosx      Point : ( π/3 , 2)

Q: Find an equation of the tangent line to the curve at the given point. x? (3,9) (Express numbers in…

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: