1. For the function f(x) = 3x? + 8x – 2, (a) Find the slope of f(x) at x = 3 | (b) Find equation of the tangent line to f(x) at x = 3.

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: Find an equation of the line L tangent to the graph of f(x) = 8x +1 at x = 1/2.

A: Calculate the y-coordinate of the point where the tangent has to be drawn. Substitute 12 for x in…

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: (a) If F(x) = 6x/(2 + x2), find F '(2) and use it to find an equation of the tangent line to the…

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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: Find f(x) if f(0) = 0 and the tangent line at (x, ƒ (x)) has the slope x(x² + 2}°.

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Q: 1. For the function f(x) = 3x² + 7x – 2, (a). Find the slope of the tangent line at x = 4. (b). Find…

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Q: 1. Consider the function f (x) = 2(3x³ – 2x²)5. %3D a. Differentiate the function. b. Find the slope…

A: 1) Given: the function fx=23x3-2x25.

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: 1. Find the equation of the tangent line to f(x) = (x-1)² 3 (x+1) when x = 2.

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Q: 2. Find the equation of the line tangent to x* – 3xy+ y³ = 1 when x = 0.

A:

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

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Q: For what values of x is the tangent line of the graph of f(x)=2x^3+9x^2+14x−12 parallel to the line…

A: Remarks; slope of two parallel line are same

Q: Find the equation of the tangent line to f-l x+4 at the point P (,0) for f(x) = 3x + 3

A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

Q: 4. Find the equation of a line tangent to f (x) = –x² – 4x at x = -1.

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Q: Find the slope of the line tangent to the given curve at the indicated point. a. f (x) = 3x + 10 at…

A: Given function,f(x)=3x+10,Aim:- To find the slope of the tangent of the curve f(x) at (-3,1)Let…

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

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Q: Find f (3) and f' (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.

A: Tangent to a function at a point is a line which just touches the graph of the function at that…

Q: Find all values of x where the slope of the tangent line to f(x)=4x^2−3x+2 is 0. x = ____

A: The detailed solution is given below Thank you

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: 3. Find the equation of the tangent line to the graph of x y + 7xy = 30 at the point (-5, 2). %3|

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Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: II. Find an equation of the tangent line to the curve of f(x) =-2x' +6x+1 when x 23

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Q: Given that f(2)=−3 and f′(2)=6, find an equation for the tangent line to the graph of y=f(x) at x=2.

A: For the function y=f(x), slope of the tangent at any point (a, f(a)) is given by mT=f'(x) at (a,…

Q: (a). For the function in this problem, find the slope of thc tangent line at the given value. f(x) =…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: (b) What is the equation of the tangent line for f(x) = x² – 1 at r = 4?

A: f(x) =x2-1

Q: 2. Find the slope of the tangent line to f(x)=V4-V+5 at the point where x 4.

A:

Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

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Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

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Q: 1) Find the slope of the tangent line to the graph of f (x) = x3 + x at x = 3.

A: Application of derivative problem

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…

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Q: 3. Find the equation of the tangent to y = 1-x² 3x+7 at the point where x = 1.

A:

Q: b) Determine the equation of the tangent line to the grap f(x) = 2x² – x + 5 at the point where x =…

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Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

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Q: What is the slope of the tangent line that touches the graph of In y + e2"- = 3y – 4r at the point…

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Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: 1. For the function f(x) = 3x² + 8x – 7, (a). Find the slope of the tangent line at x = 2. . (b).…

A:

Q: 1. For the function f(x) = 3x² + 8x – 7, (a) Find the slope of f(x) at x = 3 (b) Find equation of…

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Q: For what values of x is the tangent line of the graph of f(x) = 4x³ – 30x² + 73x parallel to the…

A: The tangent line of a curve is a straight line that touches the curve's graph at a single point. The…

Q: Let f(x) = 2x* + 3x° + 10. Find the equation of the line tangent line to the graph of Y point (1,…

A: Given  f(x) = 2X⁴ +3X³ +10 We need to find the equation of tangent of f(x) at the point (1,15)

Q: Find the exact equation of the tangent line to the curve f (x) = x³ + 3x +4 at x = 2.

A:

Q: For what values of x is the tangent line of the graph of f(x)= 2x3-12x2+2x+18 parallel to the line…

A: The tangent line of the graph of f(x)= 2x3-12x2+2x+18 is parallel to the line y=2x+.4 So, slope of…

Q: 12. Find the equation of the tangent line to f (x) = x³ at the point P(1,1).

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: For the function y= In(x² – 2) , the slope of the tangent at x = 2 is

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.