6. Find all values of x in the interval [0, 2 n] for which the slope of the tangent to y e* csc(x) is zero.

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a²x – a ln(ax +1) at z…

A:

Q: 134 Find the slope of the tangent line to the graph at the given point. Cissoid: 4y2 – xy2 = x³ %3D…

A:

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: 1. Find the slope of the tangent line for the following function at indicated point: x² – 1 S(x) =…

A: Given function: fx=x2-1x+1 Simplifying the function: fx=x2-1x+1       =x2-12x+1Using: a2-b2=a-ba+b…

Q: Find a number a such that the tangent line to the graph v= 3x at x = a is parallel to the tangent…

A:

Q: Let f(x) = 6x + 2 tangent line to the graph of f(x) at the point (0, – 3) is given by y = mx + b for…

A: The objective is to find the equation of the tangent line.

Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: Find the tangent line to g (x) 16 4T at z = 4.

A:

Q: 4. Determine an equation for the tangent line to g(x) = 3 csc(x) – 2 at a = T/4.

A: Solution :-

Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much…

A:

Q: There is only one point with a horizontal tangent line to the graph of the curve y = x + cos x in…

A:

Q: The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where…

A: Given, The tangent line to the graph of y=ln(2x) is perpendicular to x+4y=1 Here, y=ln(2x) To find…

Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

A:

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: The equation of the tangent line to the graph of f(x)=ln|x at x = -2 is v=²(x+2)+n2 (a) TRUE (b)…

A:

Q: 3. Find the slope of the tangent at x = 1 for y = ln(2x + 3) a) 2 b) = d) In(5)

A: As per Bartleby guidelines rule I am answering only first question as both question are different…

Q: If f '(1)=4, f(1)=2, and g(x)= f(x)·tan¬(x), what is the slope of the tangent line to the curve…

A: We can solve the problem by obtaining the tangent by doing derivative of the function given.

Q: Suppose f( – 1) = 3, f'(– 1) = 6 , and g(æ) = x°f(x). The tangent line to g(x) at x = 1 is given by…

A:

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x is 4

A:

Q: -1 The tangent line to the graph of y = tanh (4x) is parallel to z + y = 5 at point(s) where

A:

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Find a > 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

Q: 11 Find /(x) if ƒ (1) = and the tangent line at (x, f (x)) has the slope 1 1xe*²-1 1 Oa. O b. 1le*-1…

A: Using formula of slope of tangent & integration to find f(x)

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

A:

Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). y = In(e' + e4) O 2y + 5x…

A:

Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: 2) Find the point(s) at which the graph of f (x) = has a horizontal tangent. x2+1 %3D

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: 35. Does the graph of Sx*sin(1/x), x + 0 f(x) (o. x = 0 have a tangent line at the origin? Give…

A: Given: fx=x2sin1x,x≠00,x=0

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: What is the equation of the tangent line to the graph of f'(x) at x = 4, if f(x) = vx? O y = - + O y…

A: Topic:- application of derivatives and tangent equation

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x = is %3D

A: We need to find slope of normal line.

Q: Suppose h(x) = /f(x) and the equation of the tangent line to f(x) at x = 1 is y = 4+ 4(x – 1).

A: WE area asked to find h'(1)

Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: 1. The slope of the tangent line for the function f (x) = In x at x = 1 is: (A) (B) 1 (C) 0 (D) None…

A:

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

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

A:

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: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

A:

Q: The slope of the tangent line to the graph of y = ln x at x = a E R approaches infinity as a → 0+.

A: Given curve: y=ln x

Q: 1) Find the equation of the tangent line and normal line to the graph of the function y=x√√x-1 at…

A: As we know that; The expression for the equation of the tangent line is: y-y0=mx-x0 Where m is the…

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: 2 2х + 2х +1 G(x) = Jsech(x) y e dy

A:

Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?