Suppose f(x) = 2ax³ + b°x – 4c where a, b and c are real constants. Suppose that f has a horizontal I| tangent line at r = 2, and that the tangent line to f at r = 0 is given by y = 8x + 4. Use the given information to find all possible values for a, b, and c. Explain your reasoning.

Q: 1. Write the equation of the line tangent to f (x) =1 + e*sin(2x) when x = 0. %3D %3D

A:

Q: Find the equation of the tangent line to the graph of f(x) = 3x° + 4x² – x – 4 at x = – 1. y = help…

A: We first find f'(-1) to find the slope

Q: Find an equation of the tangent line at x = 3, assuming that f (3) = 5 and         f ,(3) = 2.

A:

Q: 3. Find the points where tangent lines are vertical or horizontal: x³ + y³ = 6xy

A: Given:- x3+y3 = 6xy To find :- Points where tangent horizontal and vertical

Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Determine the point on f(x)= 2x^e where the tangent is parallel to the line y= 2x-12

A: The equation of the curve is  f(x) = 2xe The line parallel to the tangent line on the graph of the…

Q: Find the point on the curve y=x√x for which the tangent line to the curve is perpendicular to the…

A:

Q: Find the equation of the tangent line  x2y-y3 + 6x= 8  at the (3, -2)

A:

Q: Find equation of the tan gent line to the curve f(x) = /16–4x at (3,2) a)

A: To Determine: a. Find the equation tangent line to the curve

Q: Find the equation of the tangent line to f(x)=xe2x-2 + 3 at the point (1,4).

A: Slope of a tangent of a function at a point is equal to the value of the derivative at that point.To…

Q: If f(x) = 9x2 − x3, find f '(1) and use it to find an equation of the tangent line to the curve y =…

A: Given  fx =9x2-x3  Differential both sides w.r.t x and using ddxxn=nxn-1

Q: Find the equation of the line tangent to the graph of y = 3x cos x at the point (π, −3π).

A: Given Data: Equation: y=3xcosx Point: (x1, y1)=(π, −3π) The derivative of the given equation of…

Q: Find the equation of the tangent line to f(x)=−2x−4x^−1/2+3 at the point (4,−7).

A:

Q: write the equati on of the tangent and normal line line of the curve. huow your soution 2 2 4. f CX)…

A: Given: fx=x3-3x+4 at 2,6

Q: At what point on the interval (0, 7/2) does the tangent line to the curve = 3x + V3 cos x – sinx…

A:

Q: At the given point, find the line that is tangent to the curve. 5x3y - n cos y = 6t, tangent at (1,…

A: 5x2y-πcosy=6π=ddx(5x2y-πcosy)=ddx(6π)=10xy+5x2y'+πy'siny=0=(5x2+πsiny)y'=-10xy y'=-10xy5x2+πsiny…

Q: Find the equation of the tangent line to the graph of x^2 * y^2 + 6xy =1512 at the point (-7,6)

A:

Q: . Find an equation of the tangent line to the curve y = sqrt ( 3 +x2  ) that is parallel to the line…

A:

Q: At the given point, find the slope of the curve or the line that is tangent to the curve, as…

A: Use derivative

Q: Find the equation of the tangent line to the graph ofx^2 * y^2 + 3xy =18 at the point (-2, 3)

A: The given curve is: x2+y2+3xy=18 Differentiating both sides of the equation with respect to 'x', we…

Q: Find the equation of the tangent line to the function f(x)=-3x^2-2x at the point where x=1. Give…

A:

Q: At which point on the curve y = -2 + 2et – 3x is the tangent line parallel to the line 3x – y = 5?…

A:

Q: 2. Find when f(x) = x²e* has a horizontal tangent.

A:

Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 9 and f'(2) = 3. |3D

A: GIVEN FOR A FUNCTION f(x) ,f(2) = 9            &  f'(2)=3

Q: The slope of the tangent line to the curve y at the point ( 5, is: The equation of this tangent line…

A: Given curve is : y=3x To find the slope of tangent at the point 5,35 and equation of tangent in the…

Q: ) Find the equation of the tangent f (x) = 4x - 8/x at a = 16. %3D %3D

A: Given: fx=4x-8x at x=16 For finding equation of tangent at x=16, we need to find y-coordinate for…

Q: At what point is the tangent line to the curve y = 2x perpendicular to the line x – - 2y – 8 = 0? -…

A:

Q: Find the equation of the tangent line to f(x) = 8x² – 5x – 40 at (3,17). %3D

A: Solution of the problem as follows

Q: Find the equation of the tangent line to 4x2 +y2= 8 at (1,2)

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: Find the slope of the line tangent to the graph of y = sin 2xat x = 5π/4.

A: Slope of the line tangent to the graph of y = sin 2x at x = 5π/4. y(x) = sin 2x y'(x) = (sin 2x)' =…

Q: If  F(x) = 12x/(3 + x2),  find F '(3) and use it to find an equation of the tangent line to the…

A:

Q: If f(2) = 3 andf'(2)=-1, find the equation of the tangent line when x = 2 %3D %3D %3D

A:

Q: If f(x) = 5x2 − x3,find f ' (1) and use it to find an equation of the tangent line to the curve y =…

A:

Q: Find an equation of the tangent line to the function y 3x2 at the point P(1, 3). = Soluti

A:

Q: At what point is the tangent line to the curve y = 6x² perpendicular to the line x + 2y – 8 = 0?…

A: Follow next step

Q: At what point is the tangent line to the curve y³ : = 6x² perpendicular to the line 2x + y = 2 = 0?…

A:

Q: At what point is the tangent line to the curve y = 2x to the line x - perpendicular – y – 8 = 0?…

A: Let the point is (a, b), so the slope of the tangent line to the given curve can be determined as,…

Q: Find equations of the tangent lines to the curve at the given point: f(x, y) = 4x2+y? 2

A: Given:      fx,y=4x2+y2 at 32,1          4x2+y2=0            y2=-4x2 differentiating on both sides…

Q: What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=O?

A:

Q: Find the equation of the tangent line to the function f(x)=x3+3x2+x+4 at the point where x=−2. Give…

A: we have to find tangent line at x=-2given

Q: Find the tangent line to the equation: f(x) 3x2 + 2x-1, when x= 2 %3D

A: Using equation of tangent formula.

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: Find the slope and equation of the tangent line to f(r) = 3+3x at a 3 using the definition. %3D

A:

Q: Find the equation of the tangent line to the function f(x)=−3x3−2x2−1 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1

Q: If f(x) = 9x2 – x³, find f'(1) and use it to find an equation of the tangent line to the curve y =…

A:

Q: At what point (x,y) is the tangent line to the curve y=2x2-5x+8 parallel to the line y=3x-7

A: It is given that

Q: Find the slope and equation of the tangent line to f(x) =4+2x at a 3 using the definition.

A:

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 7x2 - x³, (1, 6) y =

A: