John Wallis also invented a method of finding the tangent line, which we describe as follows: Given a graph y = f(x) passing through the point (h, k), the tangent line y = mx +b has the property that: • It passes through the point (h, k), . It is either below the curve for all other x values, or above the curve. Use this approach to find the tangent to the curve y = x² at the point where x = a.

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: Find the points on the curve y = x³ -3.5x² + 10x + 15 where the tangent is horizontal. List the…

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Q: Find the equation(s) of the tangent line(s) to the graph of 9 x – 4 xy + 16 y = %3 25 at points…

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Q: Parameterize the following portions of curves: (a) e The straight line between (-5, 3) and (11, 11).…

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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 equations of the tangent lines to the graph of y = In |x| at x = 1 and x = - 1 The equation…

A: Given,                           ....(A)

Q: Consider the following curve: x? + y2 - 4x = 8xy² +92 An equation of the tangent line to the curve…

A: Our Aim is to find an equation of the tangent line to the curve given by:-x2+y2-4x=8xy2+92 -(i) at…

Q: Find the y-intercept of the tangent line to the curve y =x at the point (2,8).

A: We have given, The curve y = x3 and the point (2, 8).

Q: Consider D2 a. + 4 4 9 Sketch and describe the graph b. Find the equation of the tangent at the…

A: The given function is: x24+y24-z29=1. To Do: (a) Sketch and describe the graph. (b) Find the…