Q3) Draw the following functions: (2-2x, x <-1 4, 1 3 1)f(x) 2)y = -sin 3

Q: what is the equation of the tangent line to xy-3y^2=1 at the point (4,1) Express numbers in eaxact…

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Q: Find_f'(x) 16. f(x) = sec² x - tan² x

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Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

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Q: An equation of the tangent line to the curve y= 4x2-8x-5 at the point (-1, 5) is O y14x-9 Oy 14x71 O…

A: The curve is given by,

Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: . How many point(s) of inflection are on che graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x² -…

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Q: (1 point) Suppose f" (x) = –16 sin(4æ) and f' (0) = –4, and f(0) = -1. -1. f(T/2) :

A: Given,f''x = -16sin4xIntegrating on both side with respect to x, we get;f'x = - 64cos4x +…

Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A: Topic - tangent lines to curve passing through Given point outside curve

Q: Find the equation of the tangent line at (3, f (3)) when f (3) = 20 and f' (3) = 4. (Use symbolic…

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Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

Q: 11. Determine the absolute extreme values of the function fx) = 2 cosx- x on the interval 0<x<2x.

A: We are authorized to solve only 1 question, please repost remaining Extrema

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Suppose f''(x) = -(sin(x)), f'(0)=6 and f(0)= -1 Find f(π/2) =?

A: Given query is to find the value of the function at indicated point.

Q: Find the equation of the tangent line to the graph of g(x) = f'(x) at x = -1 when f(x) = 5x³ + 2x² +…

A: Here, f(x)=5x3+2x2+2x

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Find the equation of a tangent line to the graph of f(x) = x² – 2X at (-2,8). TYPE IN THE EQUATION…

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Q: check uniquness and existance for fixed point while f(x)=(2x+1)^-3 in [1,2]

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Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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Q: What is the equation of the tangent line to xy – 3y = 1 at the point (4, 1)? (Express numbers in…

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Q: Find an equation of the tangent line to the graph of function f(x): 3 %3D x+5 at the point (2, ).…

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Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: Compute for the possible root of the function f(x) = x4 - x³ - x? - 4 in the interval [-2, -1]. Use…

A: The equation in the form f(x)=0 is called a transcendental equation. If the function is continuous…

Q: If f(x) = etan-¹(x²) then f'(x) at x = 1 is equal to TU 2e4

A: The explanation of answer as follows :

Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: (A) Find the absolute maxima and minima for y 4x +1 over 3 - [-V5, V5]. (B) Use the second…

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Q: Find the equation of the tangent line at (3, f(3)) when f(3) 17 and f' (3) = 4. (Use symbolic…

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Q: what is the value of x in second iteration of the function f(x) = sinx - X +5, in the interval of…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

Q: Use Secant Method to calculate the root of a function f(x) = e-*(3.2sinx – 0.5cosx) on the interval…

A: To use decant method to calculate the root of a function

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…

Q: Choose the correct value of derivative. d dx x+1 X () is equal to (Hint: Look at the note of section…

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Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

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Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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Q: 4- х, хS0 10) Determine if the function y(x) =- 3x, is differentiable at x = 0. X>0

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Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given f'x=x2+2 sin2x-2. Also given f(2) = 7.   To Find: The absolute minimum value of the function f…

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.