Find the slope and the equation of the tangent line to the graph of the function at the given value of x. 3 f(x) = -x + 3x1+x; x=2 The slope of f(x) at x=2 is.

Q: Find the equation, in slope-intercept form, of the tangent line to the graph of f(x)=e^2x-3 at the…

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Q: For the given function, (a) find the slope of the tangent line to the graph at the given point; (b)…

A: The function is given b y hx = 7x To evaluate: (a) The slope of the tangent line to the graph of the…

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= X-2 9x-4…

A: topic- equation of tangent line to curve

Q: f(x) = x2 - 3x + 5; x = 3/2, x = 2. Solve, a. Find the derivative of f at x. That is, find f′(x). b.…

A: Given function f(x)=x2-3x+5 and x=32,   x=2 To find: (a) f'(x) (b) the slope of the tangent line

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 2. X-4 8x-7 f(x) =…

A: We can solve this as follows:

Q: Determine all points on the graph of ƒ (x) = x* – x² – 1 for which a) the tangent line is…

A: Tangent line is horizontal at those points on the graph where derivative dydx=0 (1) At first we find…

Q: Find the equations of the tangent line and normal lines to the graph of the function f(x) = -4x – 3…

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Q: For f(x) = 2x - 4x + 3 find the following. (A) f'(x) (B) The slope of the graph of f at x = - 4 (C)…

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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: Use the formula below to find the slope of the tangent line to the curve at the given x-value. f(x)…

A: We can evaluate the slope of tangent by the definition of derivative process.

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: Determine the point(s), at which the graph of the function has a tangent line with the given slope.…

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Q: Find the slope of the tangent line to the graph of the given function at the given value of x. y =…

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Q: f(x) = x2 + 7 at (-1, 8). Solve, a. Find the slope of the tangent line to the graph of f at the…

A: The given function is, y=fx=x2+7,

Q: Find the equation of the line tangent to the graph off at the indicated value of x. 6 3 f(x) = Inx;…

A: In this question we have to find the equation of the line tangent to the graph of f at the indicated…

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: We find f'(x) using the chain rule

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: For the given function, find (a) the equation of the secant line through the points where x has the…

A: The given function is  f(x) = y = x2 + x x = 3,  x = 7

Q: Find the slope m and an equation of the tangent line to the graph of the function f at the specified…

A: Given:f(x)=x2x+7        at  (1,16)

Q: Fill in the blank/s:

A: point form slope: y-y1=m(x-x1)Where m=f'(x) = slope(x1, y1) is a point on the line.

Q: For the given function, find (a) the equation of the secant line through the points where x has the…

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Q: Find an equation for the tangent line to the graph of the given function at (5,18). f(x) = x2 – 7…

A: Given:

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -3 and g'(4) = 5.…

A: y=g(x) and g(4)=-3 , g'(4)=5 we have to find the tangent line of the given function y=f(x)

Q: 5x - 8 Find the equation of the tangent line to the graph of f(x) = x +1 at the point at which x =…

A: Equation of tangent line is (y-y1)=m(x-x1)

Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has a x-…

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Q: For the given function, find (a) the equation of the secant line through the points where x has the…

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Q: f(x) = x2 - 7x - 4 at (-1, 4).Solve,a. Find the slope of the tangent line to the graph of f at the…

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Q: 2. (A) Find the equation of the tangent line tof (x) = x4 – 98x² + 82 at x = -1. (B) Find the…

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Q: Find an equation of a line that is tangent to the graph of f and parallel to the given line. f(x) =…

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Q: Find the function with the given derivative whose graph passes through the point P. g'(x) = - +…

A: Given,             g'(x) =6x3 + 20x4;    P1, 5

Q: f(x) = 4x2 at (-2, 16). Solve, a. Find the slope of the tangent line to the graph of f at the given…

A: Given: fx=4x2 at -2,16

Q: Use the equation below to find the tangent line to the graph of the function f(x) = 6 − 2x^2 at the…

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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: f(x) = x2 + 4 at (-1, 5) Solve, a. Find the slope of the tangent line to the graph of f at the given…

A: fx=x2+4 a. Slope of the tangent line is the derivative of the given curve at the given point. So…

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 of f(x) = -3-3x at (-3,- 30). %3! The equation of…

A: The given equations    ,  f(x)=-3-3x2 we have to find the tangent at (-3,-30) another , f(x)=2x3 at…

Q: For the given function, (a) find the slope of the tangent line to the graph at the given point; (b)…

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Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 4x? - 8x + 4 has a tangent…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. X-2 9x - 4 f(x) =…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. X-6 3x-7 f(x) =…

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Q: Find the equation of the tangent line T(x) to the graph of the given function at the indicated…

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Q: For the given​ function, (a) find the slope of the tangent line to the graph at the given​ point;…

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Q: f(x) = 3x2 + 12x - 1; x = -2, x = 1. Solve, a) Find f′(x). b) Find the slope of the tangent line to…

A: Given f(x) = 3x2 + 12x - 1; x = -2, x = 1

Q: Find the slope of the tangent line to the graph of the given function at the given value of x. 1/2…

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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) = -6 and g'(4) = 5.…

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Q: f(x) = x2 - 7x - 4 at (-1, 4). Solve, a. Find the slope of the tangent line to the graph of f at the…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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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: