Let fx)=12– for x 2 0 and f(x) > 0 . 30. The line tangent to the graph of f at the point(k(k)) intercepts the x-axis at x-4 . What is the value of k=

Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

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Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

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Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

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: 4. Write an equation for the line tangent to the curve f(x)=" In(3x) -at x=1

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Q: Find all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

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Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

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Q: Find the points on the graph of f (x) = x3 − 3x2 + x + 4 where the tangent line has slope 10.

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Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

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Q: The slope of the tangent line to the graph of the function y = 9Va -2 at (4, 16) is -5.00 O -4.00 O…

A: Simply calculate the derivative of function at given point.

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 all points (x, y) on the graph of f(x) = x° - 4x + 15x + 10 with tangent lines parallel to the…

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

A: The slope of the tangent line to the graph of f(x) at x is m(x)=3x2-2x+1 and f(2)=4.

Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: Find a function f such that f'(x) = 2x' and the line 54x + y = 0 is tangent to the graph of f. (x) =

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Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: Find the tangent line of the function f(x) = - 4Vx at x = 4, and the point at which tangent %3D line…

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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: the line tangent to f(x)=x' 3.

A: we have to find the equation of line tangent to  f(x)=x3-x2-5      , at the point (2,-1)

Q: 3. For f(x) = x -5x-6, make a table of slopes of secant lines and make a conjecture about the slope…

A: As we know that the slope of the tangent line is given by, dydxx=a=limh→0f(a+h)-f(a)h If a = 6, then…

Q: 4. Find the slope of the line tangent to the graph of 1 f (x) = 2x4 – 32x3 + 17x2 – 9x + 4 at x 2 -…

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

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Q: The slope of the tangent line to the graph of the function y = 8Vx – 3 at (9, 21) is %3D 1.33 -2.33…

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Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: 200 Compute the equation of the line tangent to f(x)=4x2+7- x2 at X =-2. Use the form y-yı=m(x-x)…

A: Use equation of tangent line

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

A:

Q: Show that the slope of the secant line for f(x) = x 3 - 2x over[5,x] is equal to x 2 + 5x + 23. Use…

A: Given: y=fx=x3-2x; 5,x we know that slopem of secant for any given functionfx over a,b is given by…

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 a function f such that f'(x) = x4 and the line 2x - y = 3 is tangent to the graph of f.

A: Given that

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: What is the maximum slope of a tangent to the function f(x) = −x3 + 4x − 2?

A: Maximum slopes of tangent to function is 4.

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

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: Find an equation for the line tangent to the graph of f at (1, 14), where f is given by f(x) = 30 -…

A: Please refer the attached image for complete solution.

Q: 3. Find the slope of the line tangent to f(x) = In(4x² – 3) at (1,1).

A:

Q: Find an equation for the line tangent to the graph of f at (2, 28), where f is given by f(x) = 5x³ –…

A: Given function is fx=5x3-5x2+8. To find an equation of tangent line to the graph at point 2,28.…

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

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Q: The slope of the tangent line to f(x) = 3x² – 1 at x = 2 is 12. true false

A: The solution of the problem is given in the next step.

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

A:

Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

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Q: Find the point where the tangent to the graph of f(x)= -x^2-6 is parallel to the line y=4x-1

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Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

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

A: Given function is  fx=32x+1

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

A: The function f(x)=x2+2x-34. We have to find all x-values where the function f(x) has a horizontal…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.