1. Describe the relationship between the derivative of a function to the slope of the tangent line.

Q: y = 3x?+1 ; (0,1)

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Q: Are the approximating functionson tangent lines?

A: YES, the approximating functions are on tangent lines.

Q: Find the slope of the tangent line to the function f ( x ) = x ^x at x=2.  Round your answer to the…

A: Given,         The slope of the tangent line to the function fx=xx at x=2.

Q: Estimate the slope (slope rise/run) of the tangent line to the curve. N 3 4 6 N D-

A: Graph of a curve is given as- We have to determine the slope of tangent line to the curve.

Q: y D. E.

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Q: When is the tangent function undefined?

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Q: Use the definition of a derivative to find the equation of the tangent line at the given point.…

A: The equation of the tangent line is  y-7x+2=0

Q: Estimate the slope of the tangent line at the point indicated. P(x) = ex ; x=0

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Q: Estimate the slope (in y-units per x-unit) of the tangent line to the curve.

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Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

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

A: the given function is y=2-x. so to find the tangent at a specified point given (-1 , 2 ). it is…

Q: Differentiate the function and find the slope of the given tangent line f(x)=2x+5/x x=5

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Q: What is the slope of the tangent line to the graph of y=x+1/x at x=2? What is the y-intercept of…

A: According to power rule of differentiation, .

Q: What role does the derivative play in defining slopes, tangent lines, and rates of change?

A: To determine the role of derivative of a function in defining slopes, tangent lines and rate of…

Q: What is the slope of the tangent line to the graph y = a° – 3x, | at the point (x1, Y1)?

A: Our Aim is to find the slope of the tangent line to the graph y=x3-3x -(i)at the point (x1,y1),

Q: Estimate the slope of the tangent line at the point indicated.

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Q: Estimate the slope of the tangent line at the point indicated f(x) = ex :   x=0

A: Find out the slope of the tangent line at the point indicated f(x)=ex : x=0. Slope of the tangent is…

Q: Estimate the slope of the tangent line at the point indicated y(x) = 1/ (x+2) ;        x = 2

A: Solution:Given   y(x)=1x+2To find the slopeFormula:slope=dydxddxxn=nxn-1

Q: differentiate the function and find the slope of the tangent line at the given value of the…

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Q: Is the slope of the line tangent to the curve the derivative?

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Q: Describe the slope of the tangent line to the graph of f(x) = e* for the following. (a) x-- (b) x-0

A: The slope of a line is the tangent of the angle that the line makes with the x-axis. The slope of…

Q: Find the slope of the tangent line to the graph at the given point. (x2 + 4)y = 8, (-2, 1)

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Q: What is the slope of the tangent line to the graph of y x*-3x +x +2 at x-2? What is the y-coordinate…

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Q: Why are both the x-coordinate and the y-coordinate generally needed to find the slope of the tangent…

A: Given,           The x-coordinate anf y-coordinate generally needed to find the slope of the tangent…

Q: 8. What is the rate of change of the slope of the tangent line to the curve y =x – 3x2 +1 when x =…

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Q: Use the definition of derivative to find the equation of line tangent to f(x) = through 2 I = 3.

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Q: Use the fact that derivative of a function at a point is the slope of the tangent line to the graph…

A: We know that the derivative is 0  at the maximum and minimum point on the graph  From the graph we…

Q: What is the slope of the tangent line to the graph of y-(x-1)/(x+1) at x-1?

A: We have to find

Q: Please figure out the equation for the tangent line to the graph of the function at the point (9,…

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Q: 2 Write the equation of the tangent line to the graph of y =x at the point x = - 0.7.

A: Given equation is To find the equation of tangent line y=mx+b, we need to find out the slope m…

Q: Use the definition of derivative to find the slope of the tangent line to the function f(x) = V2x at…

A: Let's find.

Q: Suppose the derivative of f is f '(x)=- At what values of x does the f does have a x slope of -4.

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Q: Estimate the slope of the tangent line at the point indicated.

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Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Find the slope of the tangent to the curve f(x) = at the point where x = 4

A: Given that: f(x)=5x

Q: 3 Find the slope of the tangent to the graph of f(x) = /x+5 at the point where x= 4.

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Q: What is the slope of the tangent line to the graph of y-(x-1)/(x+1) at x-3?

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Q: What can be said about the relationship between the graph of a  function and the tangent line at a…

A: The point where the second derivarive of graph is zero is called graph of inflection.

Q: What is the slope of the tangent line to the graph of y = x^2 + 1 at the point (0, 1)?

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Q: Determine the point on the curve where the slope of tangent line to the curve is 0 or -3 a) f(x)=…

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Q: What is the slope of the tangent line to the curve y = at the point (3,)?

A: What is the slope of the tangent line to the curve y=1x at a point 3, 13 ?

Q: What is the value of the slope of the tangent line to the curve y = 2x² + x – 3 at the point (–1,…

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Q: Locate the point where the slope of tangent line to y-n 2r2 s

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Q: Why are both the x-coordinate and the y-coordinate generallyneeded to find the slope of the tangent…

A: In implicit differentiation, the result of derivative of the curve that often contains the dependent…

Q: True or false, for the graph of y=2^x, the slope of the tangent line is the same as the function…

A: slope of tangent line to a curve y = f(x) is given by          m = dydx

Q: What is the slope of the line tangent to the graph of h(x)=sqrt(x) at x=3?

A: I have given the formula for finding a slope of tangent line below the proof  And it is used in this…