Let f (x) = x3 − 3x + 1. Show that f ,(x) ≥ −3 for all x and that, for everym > −3, there are preciselytwo points where f '(x) = m. Indicate the position of these points and the corresponding tangent lines forone value of m in a sketch of the graph of f .

Q: Let f(x) tangent line to the graph of f(x) at the point (0, 0) is = 6x + 15 – 15e". Then the…

A: The given curve is: f(x)=6x+15-15ex

Q: 3. For f(x) = /2x compute the slopes of the secant lines from 16 to each of 16± 0.01, 16 +0.001, 16…

A: When x = 16, f(x) = f(16) = √(2 x 16) = 4√2 =  5.6569  hence, slope of the secant line from (16,…

Q: Determine the equation of the tangent line to the graph of g(x) =| [1- sin(re')] dt at the In z…

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Q: Find an equation of the tangent line to the graph of y = f(x) at the given x. 14. f(x) = 1 at x = 4

A: Rtyu

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

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Q: Let f(x) = 6x + 2 tangent line to the graph of f(x) at the point (0, – 3) is given by y = mx + b for…

A: The objective is to find the equation of the tangent line.

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 the value(s) of x at which f(x)=(7x^3/3)+3x^2−x+9 has a horizontal tangent line.

A: The values of x at which the given function has a horizontal tangent line can be found by evaluating…

Q: Find the slopes of the tangent lines to the graph of f(x) = 2e² at the points (0, 2) and (1, 2e).

A: See the attached file to know how to find thesthe of a tangent at the given points.

Q: Find the tangent line to g (x) 16 4T at z = 4.

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Q: Find the equation of the tangent line to the curve f(x) = - -x4 at x = 1. O T(x) = 1 + (-4)(x - 1) O…

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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: 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: Differentiate. f(x) = In ( In (8x)) f'(x) = Compute the following derivative using the method of…

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Q: Find the equation of the tangent line to the graph of f(x) = x'e- at x = 0.

A: The given function is f(x)=x9e-x at x=0.

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 the question of the that is tangent to the curve y=-3 cos2x at x= n/6. Express with exact…

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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 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 ETL for f(x) = x³ - 2x +1 at x = −1

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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: Let f(x) = v16 – x The slope of the tangent line to the graph of f(x) at the point (7, 3) is The…

A: The slope of the tangent line to the given curve is equal to the derivative of the function at the…

Q: For what values of x in [0,2pi] does the graph of f(x)= x + 2sin(x) have a horizontal tangent?

A: Horizontal tangent:The slope of a tangent of the graph of a function f (x) is df (x) ∕dx. For a…

Q: Determine the value(s) of x such that f(x)=e*-6x have a horizontal tangent line. Answer in exact…

A: Given that  function f(x) = e3x - 6x and we determine the value of x the function have horizontal…

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

A: The given function is fx=x+1. Evaluate the slope of the function at the point (3, 2) as follows.…

Q: Find a > 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

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: Determine the equation of the tangent line to the given function at the given value of x. 1) f(x) =…

A: Dear, as per company guidelines we can answer only one question at a time, kindly post other…

Q: 5. Find an equation of the tangent line to the graph of f(x) = In (2x + 1) – e* at the point where x…

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Q: Estimate the derivative of the following using simple and high- accuracy backward, forward and…

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Q: Let f (æ) = (In(z³ + 1))". Find the slope of the tangent line at x = 1. (Give your final answer as a…

A: The slope of tangent to a curve y=f(x) at a point x=a is given by f'(a)

Q: 7) Find the tangent line to the graph of f (x) = 3 – 4e * at x =0.

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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 tangent line to f(x) = ax³ at x = -1. Assume that a is a positive constant. ***

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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: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

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Q: Find the point on the graph of f(x)=ex for which the tangent line to the graph there passes through…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 67) y = In 8x2

A: Since the expression contains x, we have to find derivative with respect to x.

Q: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

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Q: Find the slope of the tangent line to f(x)=(8x-6)cos(x) at x=0.

A: The given function is: fx=8x-6cosx To find the slope of the tangent line at x=0.

Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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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 of f (x)= x² In x at 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 a formula for the tangent line to f(x) = x² – x at x = 0

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Q: Compute f '(x) and find an equation of the tangent line to the graph at x = a.

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Q: Use the forward-difference formula to approximate the derivative of f(x) = In(x) at ro 1.8 using…

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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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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: