Find an equation of the tangent line to the graph of the function at the given point. h(x) = (x² – 3)(x³ – 2x), (-2, -4) Use a graphing utility to graph the function and the tangent line in the same viewing window. See Example 5.

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -5 and g'(3) = 2.…

A: Here, y = g(x)  and g(3) = -5 i.e. when x1 = 3, then  y1 = -5 and g(3)=2 i.e. At x =3, the slope, m…

Q: Find an equation of the tangent line to the graph of the function at the given point. y = (e4x −…

A: We first have to find y'We apply exponent rule and chain rule.y'= 8(e^(4x))*(e^(4x)) -4)

Q: In the following question/s (a) find an equation of the tangent line to the graph of the function at…

A: The given function is f(x) = x3-3x The equation of the tangent line for the curve is Now, to find…

Q: Find an equation of the tangent line to the graph of the function at the given point.   y = (e3x −…

A: Given,  The equation of the curve y = e3x-42  We have to find the equation of the tangent line at…

Q: 7x Find the slope of the tangent line to the graph of f(x) = at x=2. (x+1)(x- 5)

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -5 and g'(6) = 3.…

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Q: Find an equation of the tangent line to the graph of the function at the given point. g(x) = ex5 −…

A: Given equation of curve is Differentiating with respect to x, we get We know that slope of tangent…

Q: If g(x) = xf(x), where f(4) = 9 and f'(4) = -4, find an equation of the tangent line to the graph of…

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Q: Find the equation of a tangent line to the graph of the function g(x) = 2x – x² that is parallel to…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: Lety = 4x² – 4x+3 (a) Find the equation of the tangent line to the graph of the function atX=2; (b)…

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Q: Find all values of x (if any) where the tangent line to the graph of the function is horizontal. 8)…

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Q: g(x) : 15 — х2; (1, 14)

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Q: Find the slope of the line tangent to the graph of each function at the given point. f(x) = x3 - 2x;…

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Q: Which of the following is an equation of the line tangent to the graph of f(x)=3x^2+1 at the point…

A: Please refer the attached image for complete solution.

Q: Find an equation of the tangent line to the graph of the equation at the given point. y = 9-x2; P…

A: Solve for the equation of the tangent line

Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 3 the point (2, 2.8).

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Q: A3) Find the equation of the line tangent to the graph of f(x) = 6x3 + 5x2 – 5x – 4 at z = -4. %3D

A: Firstly, we will differentiate f(x) and put x=-4 to find the slope of the equation then we will find…

Q: A) Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x = 1.

A: Here we find equation of tangent on given curve.

Q: Find the equation of the line tangent to the function at the given point. Your answer should be in…

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Q: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Given:f(x)=5x(1+x2) Formula: ddxf(x)g(x)=g (x)f'(x)-f(x)g'(x)g(x)2

Q: Write the equation of the line tangent to the graph of the following equation at x = 0. y = In (x5 +…

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Q: h(x) = -3x° – 5x + 20r + 60r

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Q: Find an equation of the tangent line to the graph of y = x(x + 3) at the point (1, 1024). 2304x –…

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Q: Find an equation of the tangent line to the graph of h(x)= 2x-x'at the point (-2, 4). Write the…

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.

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Q: Find an equation for the line tangent to the graph of f(x) = 5xe" at the point (a, f(a)) for a = 1.…

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Q: Write an equation for z' if z(x) = 3x2 + 5x + 1. Then, write the equation of the tangent line in…

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Q: Find an equation for the tangent line to the graph of the function F(x) = V3x2 + 9 at the point (3,…

A: To find the equation of tangent of given equation.

Q: Consider the function and point given below. f(x) (-1, 10) х, х* (a) Find an equation of the tangent…

A: Consider the given function:

Q: The equation 12x-0.5 = -3(y+6) represents the equation of the tangent line to the graph of g(x) when…

A: Given that, Equation of tangent to the graph of g(x) is, 12x - 0.5 = - 3(y + 6) we have to find the…

Q: Consider the given function and point. f(x)= -7x^4+11x^2-4, (1,0) A. Find an equation of the…

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Q: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=7

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Q: find an equation of the tangent line to the graph of the given point. f(×)= √x(x-8), (16,32)

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Q: Find an equation for the line tangent to the graph of the given function at the indicated point. x3…

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Q: Suppose f(5) - 9 and f'(5) = = - 3. - An object moves along the curve y³ - 3x² f(x) = 5x = 649. For…

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Q: Find the equation of a tangent line to the graph of the function g(x)=2x−x2g(x)=2x−x2 that is…

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Q: Determine all values of x for which the slope of the line tangent to y=x³ - 4x² +9x-1 is 5.

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Q: Given that f(-8) = 2 and f '(-8)  = 3, find an equation for the tangent line to the graph of y =…

A: Given that f-8=2

Q: 2x+5 2. What is the equation of the tangent line to the graph of f(x) = in x = 5? x-3

A: fx=2x+5x-3f'x=2x-3-12x+5x-32f'x=2x-6-2x-5x-32f'x=-11x-32

Q: 2x-5 Find the equation of the tangent line to the graph of f(x) = at the point at which x+1 x = 0.

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -8 and g'(4) = 71.…

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Q: Find an equation of the tangent line to the graph at the given point. 3(x2 + y?)² = 100(x² – y²),…

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Q: f(x) = 3x³ – 9x² + *+3 Determine the equation of a line parallel to the tangent to f(x) at x = 4.

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Q: please help

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Q: If g(x) - xf(x), where (4) = 9 and f'(4) = -4, find an equation of the tangent line to the graph of…

A: Given:  gx=x fxf4=9f'4=-4 To Find:  To find an equation of the tangent line to the graph of g at the…

Q: Find an equation for the tangent to the curve at the given point. y = x3/2 , (5, 62.5)

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Q: Find the equation of the tangent to the graph at the indicated point. f(x) = x2 - 6x; a = -1 y = 4x…

A: Let's find.

Q: a. Find an equation for the line perpendicular to the tangent to the curve y = x' - 9x + 4 at the…

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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: