Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x = 1, and f(2) = 6. Which statement must be correct?

Q: 1. Find the slope of the tangent line to the graph of f at x = 4, given that f(x) = -x2 + 4Vx.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: Find the equation of the tangent line to the graph of f(x) at the given point. f(x) = V12x + 4 at…

A: The function is fx=12x+4 and the point is given as 1,4. Differentiate the function with respect to…

Q: Find the tangent line to the function f (x) = x² – 4x + 5 at the point (3,2).

A: To find: The tangent line to function fx=x2-4x+5 at the point 3,2. Formula used: The slope of…

Q: 7. If the tangent line to y = f(x) at (-1,3) passes through the point (2,1), find fl-1) and f'(-1).

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Q: Find the line tangent to the graph of f(x) = x² + x +1 at xo = 2

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Q: Find the equation of the tangent line to the graph of f(x) = 2x² –In Vx at X = 1. %3D

A: First we differentiate to find the slope then use formula to find the equation

Q: The slope of the tangent line to the graph of f(x) D x2 at a = -1 is: %3D %3D

A: Given  equation of the graph  f(x) = xx2-x                        ...........(1) We have to find the…

Q: Find all value of x=c, so that the tangent line to the graph of f(x) at (c,f(c)) will be horizontal…

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Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: Find an equation of the tangent line to the graph of f (z) = -2² + 3z – 2 at the point (2, 0)

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Q: Find an equation of the tangent line to the graph of y = f 1 (x) at x = 3, where f(x) = x 4.

A: Given: f(x)=x4 at x=3  To find the tangent line of the given function at x=3

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: Find f(x) if f(2) 5 and the tangent line at x has slope (x = 1)eX- 2x. %3D f(x) =

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Q: Find the equation of the tangent line to the curve f(x) = 2x³ + 3x – 1 at x = 0. о Т(«) — За +1 Ο Τ(…

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Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

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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: Find the equation of the tangent line to the graph of f(x)=x^2cos(x) at x=0

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Q: Find the equation of the tangent line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A: The function is fx=x4+2x and x=1.  Find the derivative of the function fx=x4+2x using the limit…

Q: The equation of the tangent line to the curve of f(x) = 2x² at x = a) f(x) = 4x – 2 b) f(x) = 4x + 2…

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Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: If the slope of the tangent line to the graph of f(x) at x is m(x) = 3x<– 2x +1 and f(2)=3, then…

A: Given query is to find the value of f(-4).

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 the equation of the tangent line to the graph of f(x)=x^2(x^1/2 +1) at x=4

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Q: Find the equation of the tangent line to the graph of f(x)= 1 at the point (2,1). %3D X-1

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

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Q: Find the slope of the tangent line to the given curve at x = 3: f(x) = -V8x + 1 %3D

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Q: The slope of the tangent line for the function f(x) = x^4 – 3x^3 + x^2 – 2x + 8 at x = 1 is

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Q: find all points (x,y) on the graph of f(x)=3x^2-5x with tangent lines parallel to the line y=7x+1.

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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: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

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Q: Find an equation of the tangent line to the graph of f(x) = e×/2 In(x) at its inflection point.…

A: The point of inflection is the point where the second order derivative of the function becomes zero.…

Q: Find all x-values where f(x) = (x² + 2x – 3)4 has a horizontal tangent line.

A: We find f ' (x) using the chain rule and the power rule. f(x)=(x2+2x-3)4…

Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-x+1  and f(2)=4, then what…

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Q: Find the slope of the tangent line to the given curve at the indicated point by using the two-step…

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Q: Find the equation of the tangent line to the function f(x)=−2x3−4x2−3x+2 at the point where x=−1.…

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Q: 5. Find the tangent line to the curve of f(x)= Vx2 +8x at x = 1.

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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 all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

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Q: Find a formula for the tangent line to f(x) = x² – x at x = 0

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Q: Find an equation of the tangent line to the graph of the function f(x) = 4x – 2x3 at x = -1. Select…

A: Given: fx=4x-2x3   at x=-1

Q: Find the equation of the tangent line to f(x) =3cscx+xsinx at X= 2 A y=x- 3 y=x+3+ 2 y=x+3 y=x+3-

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Q: Suppose f(5) = 2, f'(5) = 8, and g(x) = In [f(x)+4]. Find an %3D equation of the tangent line to…

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Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1.…

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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)?

Q: Find the equation of the tangent line to the curve f(x)=5-x² at x = 2. O x-4y-2=0 O 4x + y +7=0 O 4x…

A: Find the equation of the tangent line to the curve f(x) =5-x^2 at x=2.

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: